Solve for z. z - 3 ≥ 9 or z + 12 ≤ 15 Write your answer as a compound inequality with integers. Choices: (A)z ≥ 12 or z 12 or z ≤ 3 (C)z > 12 or z < 3 (D)z ≥ 12 or z ≤ 3

Subtract to isolate z: Now, to solve for z in the inequality z + 12 ≤ 15, we need to isolate z by subtracting 12 from both sides of the inequality. z + 12 - 12 ≤ 15 - 12 z ≤ 3Combine separate inequalities: We have two separate inequalities from the original compound inequality: z ≥ 12 and z ≤ 3. Since the original statement uses ＂or,＂ we combine these two inequalities into a compound inequality. The final compound inequality is z ≥ 12 or z ≤ 3.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

z

\newline

z - 3 \geq 9

z + 12 \leq 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

z \geq 12

z < 3

\newline

(B)

z > 12

z \leq 3

\newline

(C)

z > 12

z < 3

\newline

(D)

z \geq 12

z \leq 3

Subtract to isolate $z$ : Now, to solve for $z$ in the inequality $z + 12 \leq 15$ , we need to isolate $z$ by subtracting $12$ from both sides of the inequality. $\newline$ $z + 12 - 12 \leq 15 - 12$ $\newline$ $z \leq 3$
Combine separate inequalities: We have two separate inequalities from the original compound inequality: $z \geq 12$ and $z \leq 3$ . Since the original statement uses ＂or,＂ we combine these two inequalities into a compound inequality. $\newline$ The final compound inequality is $z \geq 12$ or $z \leq 3$ .