Solving Multi-Step Equations Unit Review

Multi-Step Equations

100

Solve.  6 - 4x = 34

x = –7

200

Solve. -3/4x +5 = 11

x = -8

300

Solve.  3(x - 4) = –1/2(24 - 6x)

infinitely many solutions; x = {R} (all real numbers)

400

4(2x - 1) - 2x = –22

x = –3

500

6(x - 1) + 9 = 8(x+3) - 3

x = –9

Word Problems

100

The sum of two consecutive integers is 45.  Write an equation that can be used to find the integers. 

x + x + 1 = 45

200

The sum of two consecutive odd integers is 156.  Write an equation that can be used to find the integers. 

x + x + 2 = 156

300

The length of a rectangle is twice its width.  The perimeter of the rectangle is 96.   Write an equation that could be used to find the rectangle's dimensions. (Let x = the width).

2x + 2(2x) = 96

400

The length of a rectangle is one less than twice its width.  The perimeter of the rectangle is 22 in.  Write and solve an equation to find the rectangle's dimensions. (Let x = the width)

2x + 2(2x - 1) = 22

x = 4

The width is 4 inches and the length is 7 inches. 

500

The sum of three consecutive odd integers is 129.  Write and solve an equation to find the integers. 

x + x + 2 + x + 4 = 129

x = 41

The integers are 41, 43, and 45. 

Proportions and Percent Change

100

Solve for x.  3x - 7/4 = 7/2

x = 7

200

3x + 5/3 = x - 1/9

x = –2

300

A $59 sweater is on sale for $40.  What percent decrease is this?  (Round to the nearest tenth of a percent.) 

32.2% decrease

400

The price of a new laptop was $750 in 2022.  By 2025, the price had increased 30%.  What was the cost of a new laptop in 2025?  

The laptop cost $975 in 2025

500

Martha has a tutoring business and plans to charge 20% more in the coming year, bringing her rate up to $15.  What was Martha originally charging per hour?

Martha's original fee was $12.50 per hour. 

Literal Equations

100

Solve for x. 3x - 4n = 12

x = 4/3n + 4

200

Solve for x.  Ax - b = c

x = c + b/A

300

(x + 1)/4 = 3y

x = 12y - 1

400

Solve for x.  (x + r)/t + 1 = 0

x = –t - r

500

Solve for r.  C = 2(Pi)r

r = C/2Pi

Absolute Value Equations

100

Write two equations (without absolute value bars) that could be used to find x.  

|x + 6| = 20

x + 6 = 20; x + 6 = –20

200

Which step should be done first to solve -5|x - 3|= –50?

Divide both sides by –5

300

Solve.  2|x+7|- 3 = –13

There is no solution since the equation simplifies to |x+7| = –5

400

The solutions of an absolute value equation are 23 and 33.  Write the absolute value equation that results in these solutions. 

|x - 28| = 5

500

The solutions of an absolute value equation are –11 and 5.  Write the equation that results in these solutions. 

|x+3|=8