7th Grade Math

246 Equations and Inequalities

Write an Inequality

STATE FAIRS Dylan has $18 to ride go-karts and play games at the

state fair. If the go-karts cost $5.50, what is the most he can spend

on games?

We need to find the greatest amount of money Dylan can spend

on games.

Let x represent the amount Dylan can spend on games. Write an

inequality to represent the problem.

Words

Symbols

Inequality

Cost of cost of must be less total

go-kart plus games than or equal to amount.

5.50 + x ≤ 18

5.5 + x ≤ 18

5.5 + x ≤ 18 Write the inequality. (5.50 = 5.5)

• 5.5 - 5.5 Subtract 5.5 from each side.
  x ≤ 12.5 Simplify.
  Check by choosing an amount less than or equal to $12.50, such as
  $10. Then Dylan would spend $5.50 + $10 or $15.50 in all. Since
  $15.50 < $18, the answer is reasonable.
  So, the most Dylan can spend on games is $12.50.

e. SAVINGS Shane is saving money for a ski trip. He has $62.50, but

his goal is to save at least $100. Write and solve an inequality

to determine the least amount Shane needs to save to reach

his goal.

Examples 1 and 2 Solve each inequality.

1. c + 4 < 8 2. 14 + t ≥ 5 3. y - 9 < 11


2. 10 > x + 5 55 c + 4 ≥ 17 6. t - 7 < 25

Example 3 Solve each inequality. Graph the solution set on a number line.

7. 6 + h ≥ 12 8. 15 - y < 8 9. - 7 ≤ n + 9

Example 4 10. ELEVATORS An elevator must weigh less than 2,800 pounds. Write and

solve an inequality that describes how much weight the elevator can

gain if its current weight is 2,375 pounds.

Real-World Link

State Fairs

According to a recent

survey, corn dogs are

one of the favorite

foods of fairgoers.

They were first

invented at the Texas

State Fair about

70 years ago.

RRR

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