Page 11 - Math Course 3 (Book 1)

Adding and Subtracting Linear Inequalities

Variables on Each Side Your Turn!

Example Solve by Adding

Solve k – 4 < 10.
Solve 12n – 4 ≤ 13n. Graph the solution.
A. k > 14
12n – 4 ≤ 13n Original inequality B. k < 14
C. k < 6
12n – 4 – 12n ≤ 13n – 12n Subtract 12n from D. k > 6

each side.
–4 ≤ n Simplify. Answer

Answer Since –4 ≤ n is the same as n ≥ –4,
the solution set is {n | n ≥ –4}.
Solve by Subtracting

The temperature at the end of the day in Cleveland
–6 –5 –4 –3 –2 –1 0 had risen 15°F to a temperature less than 13°F.
What was the temperature at the beginning of the
day?
Write an Inequality to Solve a A. {m | m < –2}

Problem –5 –4 –3 –2 –1 0 1
B. {m | m > 28}
ENTERTAINMENT
Alicia wants to buy season passes to two theme 24 25 26 27 28 29 30
parks. If one season pass costs $54.99, and Alicia C. {m | m > –2}
has $100 to spend on passes, the second season
pass must cost no more than what amount?
–5 –4 –3 –2 –1 0 1
Words The total cost of the two passes must D. {m | m > 2}
be less than or equal to $100.
–1 0 1 2 3 4 5
Variable Let s = the cost of the second pass.
Answer

Is less
Inequality The total than or $100
cost
equal to
54.99 + s ≤ 100

Solve the inequality.

54.99 + s ≤ 100 Original inequality

54.99 + s – 54.99 ≤ 100 – 54.99 Subtract 54.99
from each side.

s ≤ 45.01 Simplify.

The second season pass must
Answer
cost no more than $45.01.

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