Question

what is the correct graph of the compound inequality $5x + 2 < -3$ or $2x - 6 \geq -12$?\
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\\(\bigcirc\\) a. \
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\\(\bigcirc\\) b. \
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\\(\bigcirc\\) c. \
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\\(\bigcirc\\) d. \
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\\(\bigcirc\\) e. \
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\\(\bigcirc\\) f. \
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select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
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\\(\bigcirc\\) a. the solution set in interval notation is \\(\square\\).\
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\\(\bigcirc\\) b. the solution is the empty set.

Explanation:

Step1: Solve $5x+2<-3$

Subtract 2 from both sides:
$5x < -3 - 2$
$5x < -5$
Divide by 5:
$x < -1$

Step2: Solve $2x-6\geq-12$

Add 6 to both sides:
$2x \geq -12 + 6$
$2x \geq -6$
Divide by 2:
$x \geq -3$

Step3: Combine solution sets

The compound inequality uses "or", so the solution is all $x$ where $x < -1$ or $x \geq -3$. This covers all real numbers, since every real number satisfies one of the two conditions.

Answer:

D
A. The solution set in interval notation is $(-\infty, \infty)$