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P1.1: Expressions and Equations (1.5-Day)

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Last updated almost 4 years ago
20 questions
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Question 1
1.

Match the vocabulary terms with their definitions.

Draggable itemarrow_right_altCorresponding Item
term
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the smallest mathematical unit, usually a number, a variable, or a product of numbers and variables
equation
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a group of terms joined by operations, a mathematical phrase
evaluate
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a process that takes (usually two) terms and produces a result; common ones include addition, subtraction, multiplication, and division
operation
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to assign a numerical value to, usually by substituting a numerical value for any variables in an expression
inverse function
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an operation that assigns an output to each input
expression
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a function that has the reverse outputs and inputs of another function; a function which undoes another function
function
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two expressions joined by an equal sign
Question 2
2.

Match the functions/operations with their inverses.

Draggable itemarrow_right_altCorresponding Item
multiplication
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addition
f(x) = 3(x+2)
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division
f(x) = 3x
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f-1(x) = x/3
subtraction
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f-1(x) = x + 3
f(x) = 3x + 2
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f-1(x) = \frac{1}{3}x-2
f(x) = x - 3
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f-1(x) = \frac{x-2}{3}
Question 3
3.

Put the steps in order to evaluate the following expression for x=2.

5(\frac{x+4}{3}-2)

  1. divide by 3
  2. add 4
  3. multiply by 5
  4. subtract 2
Question 4
4.

Put the steps in order to solve the following equation for x.

5(\frac{x+4}{3}-2)=0

  1. add 2
  2. multiply by 3
  3. divide by 5
  4. subtract 4
Question 5
5.

Which property justifies the following equation?

2x = 5x - 3x

Question 6
6.

Evaluate the expression for x = 5.

\frac{1}{4}(x+7) - 2x

Enter your answer as a number, no spaces.

Question 7
7.

Evaluate the expression for x = -7

|x +4| + (x+4)^{2}

Question 8
8.

Evaluate the expression for x = 12, y = -8.

\frac{1}{2}(x+y)^{2}+\frac{y}{2}

Question 9
9.

If f(x) = \frac{2-x}{2}, what is f(4)?

Enter your answer as a number, no spaces.

Question 10
10.

If f(x) = |5 - |x||, what is f(-1)?

Enter your answer as a number, no spaces.

Question 11
11.

When Dr. Demo solved the equation 2(x+4)=10, he determined that x=3. Is Dr. Demo correct? Why or why not?

Question 12
12.

Solve the equation.

2x+16=32

Enter your answer as a number, no spaces.

Question 13
13.

Solve the equation.

5(x+3) = 60

Enter your answer as a number, no spaces.

Question 14
14.

Solve the equation.

\frac{1}{3}(x+5) = 1

Enter your answer as a number, no spaces.

Question 15
15.

Solve the equation.

\frac{x+4}{2}=x+7

Enter your answer as a number, no spaces.

Question 16
16.

Solve the equation.

|2x+5|= 7

Use x={#, #} format, with exactly one space after the comma. List the smaller number first. If there is only one solution, use x={#} format. If there are no solutions, type "no solution" with no quote marks.

Question 17
17.

Solve the equation.

|15 - \frac{2}{3}x|=5

Use x={#, #} format, with exactly one space after the comma. List the smaller number first. If there is only one solution, use x={#} format. If there are no solutions, type "no solution" with no quote marks.

Question 18
18.

Solve the equation.

5-\frac{1}{2}|x|=10

Use x={#, #} format, with exactly one space after the comma. List the smaller number first. If there is only one solution, use x={#} format. If there are no solutions, type "no solution" with no quote marks.

Question 19
19.

Solve the equation.

\frac{|x+3|}{-2}=-4

Use x={#, #} format, with exactly one space after the comma. List the smaller number first. If there is only one solution, use x={#} format. If there are no solutions, type "no solution" with no quote marks.

Question 20
20.

Solve the equation.

|4-x|+10=2x+8

Use x={#, #} format, with exactly one space after the comma. List the smaller number first. If there is only one solution, use x={#} format. If there are no solutions, type "no solution" with no quote marks.