Chapter 2 Review

Writing Equations

100

Write the sentence as an equation

A number z minus twelve is equal to five

z - 12 = 5

200

Write the sentence as an equation

The sum of three times a number and four is equal to 18

3x + 4 = 18

300

Pennsylvania became a state in 1917. This was 2 years after New Jersey became a state. Which equation can be used to find the year New Jersey became a state?

y + 2 = 1917

400

Write the equation as a sentence

2(𝑡 + 4𝑞) = 2𝑞 + 4𝑡

Two times the sum of t and four times q is equal to two times q plus four times t

500

Jane is building a rectangular fence around her backyard. The length of the garden will be three times the width, and the perimeter will be 50 feet.

 

 Which equation can be used to find the width of the garden? 

Ⓐ 3w = 50

Ⓑ 8w = 50

Ⓒ 4w² = 50

Ⓓ 3w² = 50

8w = 50

One-Step Equations

100

Solve x + 5 = 20

x = 15

200

Solve x/4 = 6

x = 24

300

Solve 1/3x = 7

x = 21

400

Pennsylvania became a state in 1917. This was 2 years after New Jersey became a state. Which equation can be used to find the year New Jersey became a state? In what year did New Jersey become a state?

y + 2 = 1917; 1915

500

x/10 = 3/5

x = 6

Multi-Step Equations

100

Solve 4x + 3 = 15

x = 3

200

x/2 + 4 = 8

x = 8

300

Select all the equations that are equivalent to 

2x + 5 = –8

Ⓐ 2x = –13

Ⓑ 2x = -3

Ⓒ x = -13/2

Ⓓ x = –3/2

A; 2x = -13

C; x = -13/2

400

Solve bx + 2 = 8 for x. Assume that b ≠ 0. 

x = 6/b

500

(3x-6)/2 = 12

x = 10

Variables on Both Sides

100

Solve 2m + 7 = m + 5

m = -2

200

Solve 2(x – 4) + x = 4x + 8

x = -16

300

Solve 2x + 4 = 2(x + 4)

No Solution

400

Write and solve an equation for x so that the areas of the two figures are equal.

Shape 1 is a rectangle with a base of 4 and a height of x + 3

Shape 2 is a rectangle with a base of 5 and a height of 2x + 2

4(x+3) = 5(2x+2)

x = 1/3

500

(2x-4)/4 = 2x + 4

x = -10/3

Absolute Value Equations

100

Solve |3x - 5| = -8

No Solution

200

Solve |x + 2| - 3 = 5

x = 6        x = -10

300

2|2x-3|+5 = 15

x=4    x=-1

400

Write an absolute value equation for the following solutions

x = -2 and x = 4

|x - 1| = 3

500

At a beach, the high tide and low tide water marks can be found by solving the equation |W – 4.2| = 1.6

The high tide water mark occurs at __________ feet and the low tide water mark occurs at __________ feet.

high = 5.8

low = 2.6