1. 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.

2. 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.

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

4. 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

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.