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Unit 1: Study Guide (Due 9/25/2023)

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This is the study guide for Unit 1 covering 1.1 through 1.7


Complete the entire document and show your work for full credit.

You may use this on the test.

Day 1 9/22/23

Writing Expressions

Question 1
1.

Translate this sentence into a mathematical expression:

“the difference of 5 times a number and 4"

Question 2
2.

Translate this sentence into a mathematical expression:

“half a number plus four”

Question 3
3.

Translate this expression into English:

4x+10

Question 4
4.

Translate this expression into English:

6n-5

Simplifying Expressions

Question 5
5.

Directions: Simplify this expression.

Question 6
6.

Simplify each expression by distributing.

Question 7
7.

Directions: Simplify each expression.

Question 8
8.

Directions: Give the perimeter of each figure as a simplified expression.

Evaluating Expressions

Question 9
9.

Evaluate each expression using the variable replacements.


Question 10
10.

A scientist measures the air temperature in Death Valley, California, and records 45 °C. The expression:

1.8c + 32

gives the temperature in degrees Fahrenheit for a given temperature in degrees Celsius (c). Find the temperature in degrees Fahrenheit that is equivalent to 45 °C.


Solving Equations

Question 11
11.

Put the steps to solving this equation in the right order.

  1. Before we start solving, we identify the variable a, so we can solve for it the variable
  2. add 7 to both sides of the equation
  3. divide both sides of the equation by 3
  4. the result is x=7
Question 12
12.

Solve this equation.


Question 13
13.

What is the first step to solving this equation?

Question 14
14.

What is the second step to solving this equation?

Question 15
15.

Solve this equation.


Question 16
16.

Solve this equation.


Day 2 9/23/23

Solving Multi-Step Equations

Question 17
17.

Put the steps in the correct order to solve this multistep equation.


  1. Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
  2. The solution is a = 5
  3. Use distribution to multiply (7a+5) by -4 to get -28a - 20
  4. undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5
  5. undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
Question 18
18.

Solve this multi-step equation. Show your work (SYW)

Question 19
19.

Put the steps in the correct order to solve this multistep equation.


  1. undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4
  2. Simplify like terms to get the equation -7x - 3 = 25
  3. The solution is x = -4
  4. Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25
  5. undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28
Question 20
20.

Solve this multi-step equation. Show your work (SYW)

Solving Equations with Variables on Both Sides

Question 21
21.

What term goes in the boxes?

Question 22
22.

Fill in box 3.

Question 23
23.

Solve this equation

Question 24
24.

Solve this equation

Question 25
25.

Solve this equation

Solving and Graphing Inequalities

Question 26
26.

Solve and graph the inequality for the given variable.

Question 27
27.

Solve and graph the inequality for the given variable.

Question 28
28.

Solve and graph the inequality for the given variable.

Solving Proportions

Question 29
29.

Solve each proportion. Show your work! Or suffer the consequences...


Question 30
30.

Solve each proportion. Show your work! Or suffer the consequences...


Word Problems involving Proportion

Question 31
31.


Jasmine bought 2000 robux for $16 with her parents' money. At the same exchange rate, how many robux can Lisa buy if she stole $32 from her parents?

Word Problems involving Equations

Finding Two Numbers

Question 32
32.
The larger of two numbers is twice the smaller number. If 12 is subtracted from the larger
number, the result is 7 more than the smaller number. Find the numbers.

Smaller Number _______

Larger Number _______


Finding the Perimeter of a Rectangle

Question 33
33.
The length of a rectangle is three centimeters less than twice its width. If the perimeter of
the rectangle is 18 centimeters, find its dimensions.

Length _______

Width _______


Finding Consecutive Numbers


Question 34
34.
The sum of two consecutive numbers is 85. Find the numbers.

1st number_______

2nd number _______


Question 35
35.
The sum of three consecutive odd numbers is 57. What are the three numbers?

1st odd number_______

2nd odd number _______

3rd odd number_______