# Write Two-Step Equations ### Study Guide

Scheduled for Monday December 8 th

-Solve Equations with Rational Numbers (Lesson 1 pgs 111-117)

-Solve Two Step Equations (Lesson 2 pgs 121-128)

- Writing Two Step Equations from Word Problems (Lesson 3 pgs 129 – 136)

-Problem Solving- Working Backwards (pg 137-140)

-Solving Equations with Variables on Each side (Lesson 4 pgs 145-152)

-***NEW*** Multi-Step Equations (Lesson 5 pgs 153-160)

### Problems

Example #1-

Amy needs to rent a car for 4 days. She also decides to purchase new windshield wipers for \$16.99. If her bill at the Auto Rental Company comes to \$366.99, how much is her rental car per day?

Step 1: YOU NEED A “LET STATEMENT” in order to define your variable. We are trying to figure out the price of the rental car per day.

Let x= amount of car per day

Step 2: Amy rented the car for 4 days so 4 times x would represent the price of the rental.

Step 3: She ADDED \$16.99 to her total bill so we need to include + 16.99

Step 4: Write an equation  4x + 16.99 = 366.99 (her total)

Step 5: Solve the equation using opposite operations on BOTH sides of =

4x + 16.99 = 366.99 (undo addition first)

-16.99 -16.99

4x = 350

4x = 350

4 4 x = 87.5

Example #2-

Each question on Sheila’s math test was worth 5 points. There were also 4 bonus questions worth 1 point each. If Sheila earned a 98 out of 100 points on her test, including 3 bonus points, how many problems did she answer correctly?

Step 1: Let x= number of correct problems

Step 2: Each correct problem was 5 points, so 5 times x represents points earned. 5x

Step 3: 3 bonus points were added on to her score +3 and the total points were

90

Step 4: 5x + 3 = 98

Step 5: 5x + 3 = 98 (undo addition first)

-3 -3

5x = 95

5x = 95

5 5 x = 19 Sheila answered 19 problems correctly.

### Problem Solving- Working Backwards

Example #1-

Ms. C made brownies for her 8 th grade math class because they all studied for the test. Period 3C ate one third of the brownies and Period 4C ate half of the brownies that were left. At the end of the day, Ms. C still had 6 brownies left.

How many brownies did she bring to school?

Work backwards! We know Ms. C has 6 brownies at the end of the day. Period 4C ate half the brownies that were left. So do the OPPOSITE and double the brownies you had (x2). Period 3C ate 1/3 of the brownies so the OPPOSITE of dividing by 3 would be to multiply by 3.

6  6 x 2 = 12  12 x 3 = 36. Ms. C made 36 brownies.

Check! 36 / 3 = 12  12 / 2 = 6 (The number of brownies she had left!)

Example #2-

You NEED to get a B in math class this marking period. So far your quiz grades are

77, 80, 82, and 78. What is the lowest score you can get on your last quiz in order to guarantee an 81 average?

Use the shortcut method! The “magic number” is the average that you want to get

–- 81.

Step 1: List out the test scores  77, 80, 82, 78 and x (the last test)

Step 2: Pretend they are all an 81  81, 81, 81, 81 and 81

Step 3: Determine what you would need to add/subtract to the real scores

77 80 82 78

+4 +1 -1 +3

Step 4: Make those adjustments to the “magic number or average”

81 +4 +1 -1 +3 = 88 You must get an 88 on your last test.

Step 5: CHECK your work 77 + 80 + 82 + 78 + 88 = 405 405/5 =81

### Solving Equations with Variables on Each Side

Example #1

9g – 14 = 2g

Step 1: Subtract the smaller coefficient(# next to variable) from both sides.

9g – 14 = 2g

-2g -2g

Step 2: Solve the Equation 7g – 14 = 0

7g – 14 = 0

+14 +14

7g = 14

7 7

g = 2

Example #2

8y – 3 = 6y +17

8y – 3 = 6y +17

-6y -6y

2y – 3 = 17

2y – 3 = 17

+3 +3

2y = 20

2 2

y = 10

Example #1

Example #2

Example #3

## See Attached Reteach Practice Worksheets

### Complete for bonus points on test!

See Ms. Molinari or Mrs. Labato before/after school for extra help and review.

Good Luck!

### Lesson 1 Skills Practice

Solve Equations with Rational Coefficients

Solve each equation. Check your work.

1.

1

8 𝑥 = 5 2. 2.5𝑐 = 15.75

### Lesson 2 Skills Practice

Solve Two-Step Equations

Solve each equation. Check your solution.

1. 3 n + 4 = 7 2. 9 = 2 s + 1

3. 9 a

– 2 = –2

4.

–8 + 4 s = –16

### Write Two-Step Equations

Translate each sentence into an equation.

1. Four more than twice a number is 8.

2. Three more than four times a number is 15.

### Work Backwards:

GRADES: John had an average of 92 on her first three math tests. His scores on the second and third tests were 97 and 89. What was his score on the first test?

### Lesson 4 Skills Practice

Solve Equations with Variables on Each Side

Solve each equation. Check your solution.

1. 3 w + 6 = 4 w 2. 9 k + 6 = 8 k + 13

### Lesson 5 Skills Practice

Solve Multi-Step Equations

Solve each equation. Check your solution.

1. 6(m - 2) = 12 2. 7p – (3p + 4) = -2(2p – 1) + 10