Page 174 - Math Course 1 (Book 1)

Inequalities: More Than One Operation

Mo. 5

Lesson 6 Reverse the Inequality Symbol

Examples
KEY CONCEPTS:
1. Solve inequalities that involve more than
one operation. Solve 7 – 4a ≤ 23 – 2a and check your solution.
Graph the solution.

7 – 4a ≤ 23 – 2a Write the inequality.
MO. 5 - L6a 7 – 4a + 2a ≤ 23 – 2a + 2a Add 2a to each side.

Solving Inequalities With 7 – 2a ≤ 23 Simplify.

More Than One Operation 7 – 7 – 2a ≤ 23 – 7 Subtract 7 from
each side.
Solve a Two-Step Inequality
–2a ≤ 16 Simplify.

Examples -2a ≤ 16 Divide each side by
-2 -2 –2 and change ≤
to ≥.
Solve 5x + 13 > 83 and check your solution. Graph
the solution on a number line.
Answer a ≥ –8 Simplify.

5x + 13 > 83 Write the inequality.
Check your solution by substituting a number
5x + 13 – 13 > 83 – 13 Subtract 13 from each greater than or equal to –8.
side.
Graph the solution, a ≥ –8.
5x > 70 Simplify.

5x
> 70 Divide each side by 5.
5 5
-10 -9 -8 -7 -6

Answer x > 14 Simplify.
REAL WORLD EXAMPLE
Check 5x + 13 > 18 Write the inequality.
RUNNING
5(15) + 13 > 83 Replace x with a number José wants to run a 10k marathon.
greater than 14. Try 15. Generally, you will have enough endurance
to f nish a race that is 3 times your average
75 + 13 > 83 Simplify. daily distance. If the length of his current
daily run is 2 kilometers, how many kilometers
88 > 83 The solution checks.
should he increase his daily run to have enough
endurance for the race?
Graph the solution, x > 14.
Words 3 times 2 plus amount of increase
Answer x > 14 is greater than or equal to desired
distance
Variable Let d = the amount of increase

12 13 14 15 16 Inequality 3 • (2 + d) ≥ 10

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