PSAT: Algebra - Linear equations in one variable

If $2x + 3 = 9$, what is the value of $6x - 1$?

A factory makes 9-inch, 7-inch, and 4-inch concrete screws. During a certain day, the number of 9-inch concrete screws that the factory makes is 5 times the number $n$ of 7-inch concrete screws, and the number of 4-inch concrete screws is 22. During this day, the factory makes 100 concrete screws total. Which equation represents this situation?

What value of $p$ satisfies the equation $2p + 275 = 325$?

ID: 47140851 If $\frac{1}{2}x - \frac{1}{6}x = 1$, what is the value of $x$?

If $5 - 7(2 - 4x) = 16 - 8(2 - 4x)$, what is the value of $2 - 4x$?

ID: 98eaaec $a(3 - x) - b = -1 - 2x$
In the equation above, $a$ and $b$ are constants. If the equation has infinitely many solutions, what are the values of $a$ and $b$?

If $x = 7$, what is the value of $x + 20$?

ID: b384738a $66x = 66x$
How many solutions does the given equation have?

If $\dfrac{x-5}{7} = \dfrac{x-5}{9}$, the value of $x-5$ is between which of the following pairs of values?

ID: 039469e8 What value of $x$ is the solution to the equation $16x + 24 = 24x$?

If $x = 40$, what is the value of $x + 6$?

Lorenzo purchased a box of cereal and some strawberries at the grocery store. Lorenzo paid $2 for the box of cereal and $1.90 per pound for the strawberries. If Lorenzo paid a total of $9.60 for the box of cereal and the strawberries, which of the following equations can be used to find $p$, the number of pounds of strawberries Lorenzo purchased? (Assume there is no sales tax.)

3 more than 8 times a number $x$ is equal to 83. Which equation represents this situation?

$2.6 + x = 2.8$
What value of $x$ is the solution to the given equation?

The perimeter of an isosceles triangle is 83 inches. Each of the two congruent sides of the triangle has a length of 24 inches. What is the length, in inches, of the third side?

ID: c925cab3 A manager is responsible for ordering supplies for a shaved ice shop. The shop's inventory starts with $4,500$ paper cups, and the manager estimates that $70$ of these paper cups are used each day. Based on this estimate, in how many days will the supply of paper cups reach $1,700$?

$2(kx - n) = -\frac{28}{15}x - \frac{36}{19}$
In the given equation, $k$ and $n$ are constants and $n > 1$. The equation has no solution. What is the value of $k$?

The cost to rent a commercial fishing boat from a certain company is $950 for the first 2 hours and an additional $50 per hour for each hour after the first 2 hours. If the total cost to rent the commercial fishing boat from the company for $t$ hours, where $t > 2$, is $1,100, which equation represents this situation?

A gym charges its members a onetime $36 enrollment fee and a membership fee of $19 per month. If there are no charges other than the enrollment fee and the membership fee, after how many months will a member have been charged a total of $188 at the gym?

A science teacher is preparing the 5 stations of a science laboratory. Each station will have either Experiment A materials or Experiment B materials, but not both. Experiment A requires 6 teaspoons of salt, and Experiment B requires 4 teaspoons of salt. If $x$ is the number of stations that will be set up for Experiment A and the remaining stations will be set up for Experiment B, which of the following expressions represents the total number of teaspoons of salt required?

What value of $t$ is the solution to the equation $0.8t - 0.46 = 8(t - 0.001) + 1.9$?

If $46 = 16 + 2(x - 8)$, what is the value of $2(x - 8)$?

A company that creates and sells tape dispensers calculates its monthly profit, in dollars, by subtracting its fixed monthly costs, in dollars, from its monthly sales revenue, in dollars. The equation $15{,}000 = 2.00x - 4{,}500$ represents this situation for a month where $x$ tape dispensers are created and sold. Which statement is the best interpretation of $2.00x$ in this context?

If $3x = 30$, what is the value of $3x - 12$?

$4x + 6 = 18$
Which equation has the same solution as the given equation?

$2n + 6 = 14$A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years $n$ it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?

If $3x - 8 = 7$, what is the value of $3x + 8$?

On the first day of a semester, a film club has 90 members. Each day after the first day of the semester, 10 new members join the film club. If no members leave the film club, how many total members will the film club have 4 days after the first day of the semester?

$-3x + 21px = 84$
In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

ID: b25007fd If $4x + 2 = 12$, what is the value of $16x + 8$?

$w + 7 = 357$
What value of $w$ is the solution to the given equation?

ID: 641b9e82

In the given equation, $b$ is a constant. If the equation has no solution, what is the value of $b$?

$(p + 3) + 8 = 10$
What value of $p$ is the solution to the given equation?

What value of $p$ satisfies the equation $5p + 180 = 250$?

If $5x = 20$, what is the value of $15x$?

If $7x = 28$, what is the value of $8x$?

If $9(4-3x)+2 = 8(4-3x)+18$, what is the value of $4-3x$?

A principal used a total of 25 flags that were either blue or yellow for field day. The principal used 20 blue flags. How many yellow flags were used?

Henry receives a $\$60.00$ gift card to pay for movies online. He uses his gift card to buy 3 movies for $\$7.50$ each. If he spends the rest of his gift card balance on renting movies for $\$1.50$ each, how many movies can Henry rent?

If $\dfrac{x+6}{3} = \dfrac{x+6}{13}$, the value of $x + 6$ is between which of the following pairs of values?

ID: ab4ade30 A librarian has 43 books to distribute to a group of children. If he gives each child 2 books, he will have 7 books left over. How many children are in the group?

$10 = 2x + 4$
How many solutions exist to the equation shown above?

$3x + 21 = 3x + k$
In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

John paid a total of $165 for a microscope by making a down payment of $37 plus $p$ monthly payments of $16 each. Which of the following equations represents this situation?

$3x + 5(x + 4) = 76$
What value of $x$ is the solution to the given equation?

If $4x - 28 = -24$, what is the value of $x - 7$?

If $\frac{6}{7}p + 18 = 54$, what is the value of $7p$?

One pound of grapes costs $2. At this rate, how many dollars will $c$ pounds of grapes cost?

If $4x = 3$, what is the value of $24x$?

A museum rents tablets to visitors. The museum earns revenue of $14 for each tablet rented for the day. On Wednesday, the museum earned $406 in profit from renting tablets after paying daily expenses of $112. How many tablets did the museum rent on Wednesday? (profit = total revenue − total expenses)

If $2(x - 5) + 3(x - 5) = 10$, what is the value of $x - 5$?

If $3x - 27 = 24$, what is the value of $x - 9$?

A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?

$16x + 30 = 190$
Which equation has the same solution as the given equation?

$7(2x - 3) = 63$
Which equation has the same solution as the given equation?

$2(p+1)+8(p-1)=5p$
What value of $p$ is the solution of the equation above?

For what value of $w$ does $w - 10 = 2(w + 5)$?

$8x - 7x + 130 = 260$
What value of $x$ is the solution to the given equation?

$13x = 112 - x$
What value of $x$ is the solution to the given equation?

$x + 40 = 95$
What value of $x$ is the solution to the given equation?

If $5(x + 4) = 4(x + 4) + 29$, what is the value of $x + 4$?

Nasir bought 9 storage bins that were each the same price. He used a coupon for $63 off the entire purchase. The cost for the entire purchase after using the coupon was $27. What was the original price, in dollars, for 1 storage bin?

If $8x = 6$, what is the value of $72x$?

$k + 12 = 336$
What is the solution to the given equation?

$8x = 88$
What value of $x$ is the solution to the given equation?

If $6n = 12$, what is the value of $n + 4$?

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

In the given equation, $s$ and $r$ are constants, and $s > 0$. If the equation has infinitely many solutions, what is the value of $s$?
$\dfrac{12x + 28}{4} - \dfrac{s}{13} = r(x - 8)$

If $6 + x = 9$, what is the value of $18 + 3x$?

If $4x - \dfrac{1}{2} = -5$, what is the value of $8x - 1$?

If $2 + x = 60$, what is the value of $16 + 8x$?

A candle is made of 17 ounces of wax. When the candle is burning, the amount of wax in the candle decreases by 1 ounce every 4 hours. If 6 ounces of wax remain in this candle, for how many hours has it been burning?

How many solutions does the equation $10(15x - 9) = -15(6 - 10x)$ have?

An agricultural scientist studying the growth of corn plants recorded the height of a corn plant at the beginning of a study and the height of the plant each day for the next 12 days. The scientist found that the height of the plant increased by an average of $1.20$ centimeters per day for the 12 days. If the height of the plant on the last day of the study was $36.8$ centimeters, what was the height, in centimeters, of the corn plant at the beginning of the study?

A manufacturing plant makes 10-inch, 9-inch, and 7-inch frying pans. During a certain day, the number of 10-inch frying pans that the manufacturing plant makes is 4 times the number $n$ of 9-inch frying pans it makes, and the number of 7-inch frying pans it makes is 10. During this day, the manufacturing plant makes 100 frying pans total. Which equation represents this situation?

$\dfrac{1}{4}(x+5)-\dfrac{1}{3}(x+5)=-7$
What value of $x$ is the solution to the given equation?

What is the solution to the equation $2x + 3 = 7$?

$-49x = -98x$
How many solutions does the given equation have?

$4x + 12 = \dfrac{a(x + 3)}{2}$
In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

The perimeter of an isosceles triangle is 36 feet. Each of the two congruent sides of the triangle has a length of 10 feet. What is the length, in feet, of the third side?

The width of a rectangular dance floor is $w$ feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of $w$?

If $\dfrac{x}{8} = 5$, what is the value of $\dfrac{8}{x}$?

$3(2x - 6) - 11 = 4(x - 3) + 6$
If $x$ is the solution to the equation above, what is the value of $x - 3$?

The equation $9x + 5 = a(x + b)$, where $a$ and $b$ are constants, has no solutions. Which of the following must be true?
I. $a = 9$
II. $b = 5$
III. $b \ne \frac{5}{9}$

A line segment that has a length of 115 centimeters (cm) is divided into three parts. One part is 47 cm long. The other two parts have lengths that are equal to each other. What is the length, in $\text{cm}$, of one of the other two parts of equal length?

$\frac{4x}{5} = 20$
In the equation above, what is the value of $x$?

Which of the following is equivalent to $4x + 6 = 12$?

$2x + 16 = a(x + 8)$
In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

Megan's regular wage at her job is $p$ dollars per hour for the first 8 hours of work in a day plus 1.5 times her regular hourly wage for work in excess of 8 hours that day. On a given day, Megan worked for 10 hours, and her total earnings for that day were $137.50. What is Megan's regular hourly wage?

$\frac{1}{3}(x+6)-\frac{1}{2}(x+6)=-8$
What value of $x$ is the solution to the given equation?

If $\dfrac{2n}{5} = 10$, what is the value of $2n - 1$?

If $2(x-5)+3(x-5)=10$, what is the value of $x-5$?

If $3x - 27 = 24$, what is the value of $x - 9$?

A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?

$16x + 30 = 190$
Which equation has the same solution as the given equation?

$7(2x - 3) = 63$
Which equation has the same solution as the given equation?

$2(p + 1) + 8(p - 1) = 5p$
What value of $p$ is the solution of the equation above?

For what value of $w$ does $w - 10 = 2(w + 5)$?

$8x - 7x + 130 = 260$
What value of $x$ is the solution to the given equation?

$13x = 112 - x$
What value of $x$ is the solution to the given equation?

$x + 40 = 95$
What value of $x$ is the solution to the given equation?

If $5(x + 4) = 4(x + 4) + 29$, what is the value of $x + 4$?

Nasir bought 9 storage bins that were each the same price. He used a coupon for $63 off the entire purchase. The cost for the entire purchase after using the coupon was $27. What was the original price, in dollars, for 1 storage bin?

If $8x = 6$, what is the value of $72x$?

$k + 12 = 336$
What is the solution to the given equation?

$8x = 88$
What value of $x$ is the solution to the given equation?

If $6n = 12$, what is the value of $n + 4$?

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

In the given equation, $s$ and $r$ are constants, and $s > 0$. If the equation has infinitely many solutions, what is the value of $s$?
$\dfrac{12x + 28}{4} - \dfrac{s}{13} = r(x - 8)$

If $6 + x = 9$, what is the value of $18 + 3x$?

If $4x - \dfrac{1}{2} = -5$, what is the value of $8x - 1$?

If $2 + x = 60$, what is the value of $16 + 8x$?

A candle is made of 17 ounces of wax. When the candle is burning, the amount of wax in the candle decreases by 1 ounce every 4 hours. If 6 ounces of wax remain in this candle, for how many hours has it been burning?

How many solutions does the equation $10(15x - 9) = -15(6 - 10x)$ have?

An agricultural scientist studying the growth of corn plants recorded the height of a corn plant at the beginning of a study and the height of the plant each day for the next 12 days. The scientist found that the height of the plant increased by an average of $1.20$ centimeters per day for the 12 days. If the height of the plant on the last day of the study was $36.8$ centimeters, what was the height, in centimeters, of the corn plant at the beginning of the study?

A manufacturing plant makes 10-inch, 9-inch, and 7-inch frying pans. During a certain day, the number of 10-inch frying pans that the manufacturing plant makes is 4 times the number $n$ of 9-inch frying pans it makes, and the number of 7-inch frying pans it makes is 10. During this day, the manufacturing plant makes 100 frying pans total. Which equation represents this situation?

$\dfrac{1}{4}(x+5)-\dfrac{1}{3}(x+5)=-7$
What value of $x$ is the solution to the given equation?

What is the solution to the equation $2x + 3 = 7$?

$-49x = -98x$
How many solutions does the given equation have?

$4x + 12 = \dfrac{a(x+3)}{2}$
In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

The perimeter of an isosceles triangle is $36$ feet. Each of the two congruent sides of the triangle has a length of $10$ feet. What is the length, in feet, of the third side?

The width of a rectangular dance floor is $w$ feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of $w$?

If $\dfrac{x}{8} = 5$, what is the value of $\dfrac{8}{x}$?

$3(2x-6)-11=4(x-3)+6$
If $x$ is the solution to the equation above, what is the value of $x-3$?

The equation $9x + 5 = a(x + b)$, where $a$ and $b$ are constants, has no solutions. Which of the following must be true?
I. $a = 9$
II. $b = 5$
III. $b \ne \dfrac{5}{9}$

A line segment that has a length of $115$ centimeters (cm) is divided into three parts. One part is $47$ cm long. The other two parts have lengths that are equal to each other. What is the length, in $cm$, of one of the other two parts of equal length?

$\frac{4x}{5} = 20$
In the equation above, what is the value of $x$?

Which of the following is equivalent to $4x + 6 = 12$?

$2x + 16 = a(x + 8)$
In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

Megan’s regular wage at her job is $p$ dollars per hour for the first 8 hours of work in a day plus 1.5 times her regular hourly wage for work in excess of 8 hours that day. On a given day, Megan worked for 10 hours, and her total earnings for that day were $137.50. What is Megan’s regular hourly wage?

$\frac{1}{3}(x+6)-\frac{1}{2}(x+6)=-8$
What value of $x$ is the solution to the given equation?

If $\dfrac{2n}{5} = 10$, what is the value of $2n-1$?

$6x + k = 6x + 5$
In the given equation, $k$ is a constant. If the equation has infinitely many solutions, what is the value of $k$?

If $2x = 12$, what is the value of $9x$?

How many solutions does the equation $12(x - 3) = -3(x + 12)$ have?

If $2(3t - 10) + t = 40 + 4t$, what is the value of $3t$?

$4x + 5 = 165$
What is the solution to the given equation?

If $3x + 2 = 8$, what is the value of $9x + 6$?

$3(kx + 13) = \frac{48}{17}x + 36$
In the given equation, $k$ is a constant. The equation has no solution. What is the value of $k$?

A bowl contains 20 ounces of water. When the bowl is uncovered, the amount of water in the bowl decreases by 1 ounce every 4 days. If 9 ounces of water remain in this bowl, for how many days has it been uncovered?

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, $m$, he should drive each week?