Intermediate Algebra (11th edition)

Solving a Linear Inequality by Using the Distributive Property

Solve , and graph the solution set.

Step 1

Distributive property

Combine like terms.

Step 2 Add x.

Combine like terms.

Add 10.

Combine like terms.

Step 3

Divide by.

Change to

x...-

17

2

Ú ....

• 2

- 2 x

- 2

...

17

- 2

- 2 xÚ 17

- 2 x- 10 + 10 Ú 7 + 10

- 2 x- 10 Ú 7

- 3 x- 10 +xÚ 7 - x+x

- 3 x- 10 Ú 7 - x

- 3 x- 12 + 2 Ú 7 - x

- 31 x+ 42 + 2 Ú 7 - x

- 31 x+ 42 + 2 Ú 7 - x

EXAMPLE 4

SECTION 2.5 Linear Inequalities in One Variable 95

Solving a Linear Inequality

Step 1 Simplify each side separately.Clear parentheses, fractions, and

decimals using the distributive property, and combine like terms.

Step 2 Isolate the variable terms on one side.Use the addition property

of inequality to get all terms with variables on one side of the in-

equality and all numbers on the other side.

Step 3 Isolate the variable.Use the multiplication property of inequality

to change the inequality to one of these forms.

x 6 k, x... k, x 7 k, or xÚ k

NOW TRY
EXERCISE 4
Solve and graph the solution
set.

5 - 21 x- 42 ... 11 - 4 x

NOW TRY ANSWER

4. 1 - q, - 14

–3 –2 –1 0 1

Be sure to reverse

the inequality

symbol.

FIGURE 13shows the graph of the solution set, A-q, -^172 D.

–11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0

FIGURE 13 NOW TRY

NOTE In Step 2 of Example 4,if we add 3x(instead of x) to both sides of the in-

equality, we have the following sequence of equivalent inequalities.

Add 3x.

Combine like terms.

Subtract 7.

Combine like terms.

Divide by 2;

The result, “ is greater than or equal to x,” means the same as “xis less than or

equal to -^172 .” Thus, the solution set is the same.

-^172

• a
  b =-

a

- b

17

2

Úx

- 17 Ú 2 x

- 10 - 7 Ú 2 x+ 7 - 7

- 10 Ú 2 x+ 7

- 3 x- 10 + 3 xÚ 7 - x+ 3 x