12-5: Solving Inequalities by
Adding and Subtracting
Steps in Solving
To solve an Inequality by adding or subtracting…
I. You can solve addition and subtraction inequalities the same way as you solve equations (inverse operations).
II. Solutions to inequalities must always include the given variable and the inequality sign.
III. Write inequalities and express solutions, with variables on the left side of the inequality sign.
Problems/Examples of
Solve each inequality using inverse operations and graph your solutions.
A)
k + 3 > -2
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B)
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u – 5  -3
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r – 9  12
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c+6<2
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E) Katya has $12 to take to the bowling alley. If the shoe rental costs $3.75, what is the most she can
spend on games and snacks?
Write an inequality equation that can be used to find the solution and solve.
Write and Graph your solution.
Inequality: ________________________
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Solve each inequality using inverse operations and graph your solutions.
F)
n – 7 ≤ 15
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G) a – 10 ≥ -3
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H) d = 11 > 6
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b + 12 ≤ 19
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Edgar’s August profit of $137 was at least $20 higher than his July profit. What was July’s profit?
Write an inequality equation that can be used to find the solution and solve.
Write and Graph your solution.
Inequality: ________________________
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Solve each inequality using inverse operations and graph your solutions.
K)
x – 4 > 17
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z – 27 ≤ 19
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M) There are at least 17 more bus riders than walkers in a class. If there are 7 walkers, how many
bus riders are there?
Write an inequality equation that can be used to find the solution and solve.
Write and Graph your solution.
Inequality: ________________________
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