EXAMPLE 3 Solve an inequality with a variable on one side

Fair

You have $50 to spend at a county fair. You spend $20 for admission. You want to play a game that costs $1.50. Describe the possible numbers of times you can play the game.

SOLUTION

STEP 1

Write a verbal model. Then write an inequality.

EXAMPLE 3 Solve an inequality with a variable on one side

An inequality is 20 + 1.5g ≤ 50.

STEP 2 Solve the inequality.

20 + 1.5g ≤ 50

1.5g ≤ 30

g ≤ 20

Write inequality.

Subtract 20 from each side.

Divide each side by 1.5.

ANSWER

You can play the game 20 times or fewer.

EXAMPLE 4 Solve an inequality with a variable on both sides

Solve 5x + 2 > 7x – 4. Then graph the solution.

5x + 2 > 7x – 4

– 2x + 2 > – 4

– 2x > – 6

x < 3

Write original inequality.

Subtract 7x from each side.

Subtract 2 from each side.Divide each side by – 2 and reverse the inequality.

ANSWERThe solutions are all real numbers less than 3. The graph is shown below.

GUIDED PRACTICE for Examples 3 and 4

Solve the inequality. Then graph the solution.

5. 4x + 9 < 25

4x + 9 < 25 Write original inequality.

4x < 16 Subtract 9 from each side.

x < 4 Divide each side by 4.

6. 1 – 3x ≥ – 14

1 – 3x ≥ – 14 Write original inequality.

– 3x ≥ – 15 Subtract –1 from each side.

x ≤ 5

GUIDED PRACTICE for Examples 3 and 4

Solve the inequality. Then graph the solution.

7. 5x – 7 ≤ 6x

8. 3 – x > x – 9

5x – 7 ≤ 6x Write original inequality.

x > – 7 Subtract 5x from each side.

3 – x > x – 9 Write original inequality.

3 – 2x > – 9

– 2x > – 12

x < 6

Subtract x from each side.

Subtract 3 from each side.

Divide each side by –2 and reverse.