Solve and graph inequalities

Learning to solve and graph inequalities is easy and straightforward once you know how to solve two-step equations.

Example #1:

Solve x + 3 < 9

x + 3 < 9

Subtract 3 from each side of the equation

x + 3 - 3 < 9 - 3

x + 0 < 6

x < 6

Graph the solution

x is smaller than 6

Check:

Choose a point on the graph such as 4.

4 + 3 = 7 and 7 is smaller than 9

Example #2:

Solve 5x - 2 ≥ 13

5x - 2 ≥ 13

Add 2 to each side of the equation

5x - 2 + 2 ≥ 13 + 2

5x + 0 ≥ 15

5x  ≥ 15

Divide each side by 5

5x/5  ≥ 15/5

x  ≥ 3

Graph the solution

x is bigger than or equal to 3

Notice how this time the circle is shaded at 3 meaning that 3 is included in the solution.

Check:

Choose a point on the graph such as 7.

5(7) - 2 = 35 - 2 = 33 and 33 is bigger than 7.

Example #3:

Solve 2 + 3(5 - x)  ≥ 38

2 + 3(5 - x)  ≥ 38

Use the distributive property 

2 + 15 - 3x  ≥ 38

Simplify by adding 2 and 15

17 - 3x  ≥ 38

Subtract 17 from each side of the equation

17 - 17 - 3x  ≥ 38 - 17

0 - 3x  ≥ 21

-3x  ≥ 21

Divide each side by -3 and reverse the inequality

-3x/-3  ≤ 21/-3

x ≤ -7

Graph the solution

x is smaller than or equal to negative seven

Check:

Choose a point on the graph such as -10.

2 + 3(5 - -10) = 2 + 3(5 + +10) = 2 + 3(15) = 2 + 45 = 47 and 47 is bigger than 38.

Recent Articles

  1. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes