How to Solve Multi-Step Inequalities? (+FREE Worksheet!)

To solve multi-step inequalities you need to do more than one math operation. Learn how to solve Multi-Step inequalities in a few simple steps.

How to Solve Multi-Step Inequalities? (+FREE Worksheet!)

Related Topics

Step by step guide to solve multi-step inequalities

  • Isolate the variable similar to equations.
  • Simplify using the inverse of addition or subtraction.
  • Simplify further by using the inverse of multiplication or division.
  • For dividing or multiplying both sides by negative numbers, flip the direction of the inequality sign.

Multi–Step Inequalities – Example 1:

Solve this inequality. \(4x-8 > 24\)

Solution:

First add \(8\) to both sides: \( 4x-8 > 24→ 4x-8+8 > 24+8\)
Then simplify: \(4x-8+8 > 24+8→4x > 32\)
Now divide both sides by \(4: \frac{4x}{4} > \frac{32}{4 } →x > 8\)

Multi–Step Inequalities – Example 2:

Solve this inequality.  \(2x + 6 \leq10\)

Solution:

First subtract \(6\) from both sides: \(2x + 6 \leq10\) → \(2x+6−6≤10−6\)
Then simplify: \(2x+6−6≤10−6→2x≤4\)
Now divide both sides by \(2: \frac{2x}{2}≤\frac{4}{2} →x≤2\)

Multi–Step Inequalities – Example 3:

Solve this inequality. \(2x-2≤6\)

Solution:

First add \(2\) to both sides: \(2x-2≤6\) → \(2x-2+2≤6+2\)

Then simplify: \(2x-2+2≤6+2→2x≤8\)
Now, divide both sides by \(2: \frac{2x}{2}≤\frac{8}{2}→x≤4\)

Multi–Step Inequalities – Example 4:

Solve this inequality. \(-2x-4 < 8\)

Solution:

First add \(4\) to both sides: \(-2x-4 < 8\) → \(-2x-4+4 < 8+4\)
Then simplify: \(-2x-4+4 < 8+4→-2x < 12\)
Now divide both sides by \(-2\) (Remember, for dividing or multiplying both sides by negative numbers, flip the direction of the inequality sign.)

\(\frac{-2x}{-2} > \frac{12}{-2 } →x > -6\)

Exercises for Solving Multi–Step Inequalities

Solve each inequality.

  1. \(\color{blue}{\frac{9x}{7} – 7 < 2} \\ \)
  2. \(\color{blue}{\frac{4x + 8}{2} ≤ 12} \\ \)
  3. \(\color{blue}{\frac{3x – 8}{7} > 1} \\ \)
  4. \(\color{blue}{–3 (x – 7) > 21} \\ \)
  5. \(\color{blue}{4 + \frac{x}{3} < 7} \\ \)
  6. \(\color{blue}{\frac{2x + 6}{4} ≤ 10} \\ \)

Download Multi-Step Inequalities Worksheet

This image has an empty alt attribute; its file name is answer-3.png

Answers

  1. \(\color{blue}{x < 7 }\)
  2. \(\color{blue}{x ≤ 4 }\)
  3. \(\color{blue}{x > 5}\)
  4. \(\color{blue}{x < 0 }\)
  5. \(\color{blue}{x < 9}\)
  6. \(\color{blue}{x ≤ 17}\)

Related to "How to Solve Multi-Step Inequalities? (+FREE Worksheet!)"

Managing Math Fear as an Adult
How to Handle Your Math Assignments?
How to Choose the Best Backup Software Solution for School Districts?
How to Find the Volume and Surface Area of a Triangular Pyramid?
How to Convert a Linear Equation in Standard Form to Slope-Intercept Form?
How to Find Values of Functions from Graphs?
How to Find the Unit Price of a Product?
How to Divide Decimals by Whole Numbers?
How to Find the Volume and Surface Area of Triangular Prism?
How to Find Elapsed Time?

What people say about "How to Solve Multi-Step Inequalities? (+FREE Worksheet!)"?

  1. I don’t understand how Question 4 is x

Leave a Reply

X
30% OFF

Huge Discount!

30% OFF

Take It Now!

SAVE $5

It was $16.99 now it is $11.99