Solve for g. g - 10 ≤ -14 or g - 12 ≥ 1 Write your answer as a compound inequality with integers. Choices: (A)g ≤ -24 or g ≥ 13 (B)g ≤ -24 or g ≥ -11 (C)g ≤ -4 or g ≥ -11 (D)g ≤ -4 or g ≥ 13

Addition to isolate g: To isolate g in the inequality g - 10 ≤ -14, we need to add 10 to both sides of the inequality. g - 10 + 10 ≤ -14 + 10 g ≤ -4Addition to isolate g: To isolate g in the inequality g - 12 ≥ 1, we need to add 12 to both sides of the inequality. g - 12 + 12 ≥ 1 + 12 g ≥ 13Compound inequality solution: Now we have two separate inequalities that form the compound inequality: g ≤ -4 or g ≥ 13 This is the solution to the given problem.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

g

\newline

g - 10 \leq -14

g - 12 \geq 1

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Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

g \leq -24

g \geq 13

\newline

(B)

g \leq -24

g \geq -11

\newline

(C)

g \leq -4

g \geq -11

\newline

(D)

g \leq -4

g \geq 13

Addition to isolate $g$ : To isolate $g$ in the inequality $g - 10 \leq -14$ , we need to add $10$ to both sides of the inequality. $\newline$ $g - 10 + 10 \leq -14 + 10$ $\newline$ $g \leq -4$
Addition to isolate $g$ : To isolate $g$ in the inequality $g - 12 \geq 1$ , we need to add $12$ to both sides of the inequality. $\newline$ $g - 12 + 12 \geq 1 + 12$ $\newline$ $g \geq 13$
Compound inequality solution: Now we have two separate inequalities that form the compound inequality: $\newline$ $g \leq -4$ or $g \geq 13$ $\newline$ This is the solution to the given problem.