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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
Answers
GPT-4o mini
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 \( g < 34 \).
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 \( g < 34 \).