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Quiz: Inequalities and Their Graphs
CR Algebra 1 A (GP) 24-25 / 7:Solving Inequalities
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7.
Solve the inequality.

g + 2 – 2(g – 16) > 0

g < 34

g > –30

g > 34

g < –30

1 answer

To solve the inequality \( g + 2 - 2(g - 16) > 0 \), let's simplify it step by step.

  1. Distribute the \(-2\) in the term \( -2(g - 16) \): \[ g + 2 - 2g + 32 > 0 \]

  2. Combine like terms: \[ -g + 34 > 0 \]

  3. Rearrange the inequality to isolate \(g\): \[ -g > -34 \]

  4. Multiply both sides of the inequality by \(-1\) (remember that when you multiply or divide by a negative number, you flip the inequality sign): \[ g < 34 \]

Thus, the solution to the inequality is \( g < 34 \).