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.