Solve for w. w - 9 > 4 or w + 20 ≤ 12 Write your answer as a compound inequality with integers. Choices: (A)w > 13 or w ≤ -8 (B)13 > w > -8 (C)13 > w ≥ -8 (D)w > 13 or w < -8

Isolate w in first inequality: First, let's solve the inequality w - 9 > 4. To isolate w, we need to add 9 to both sides of the inequality. w - 9 + 9 > 4 + 9 w > 13Isolate w in second inequality: Now, let's solve the second inequality w + 20 ≤ 12. To isolate w, we need to subtract 20 from both sides of the inequality. w + 20 - 20 ≤ 12 - 20 w ≤ -8Combine inequalities using OR: We have two separate inequalities from the original problem: w > 13 and w ≤ -8. Since the original problem states ＂or＂ between the inequalities, we combine them using ＂or＂. The compound inequality is w > 13 or w ≤ -8.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

w

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w - 9 > 4

w + 20 \leq 12

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

w > 13

w \leq -8

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(B)

13 > w > -8

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(C)

13 > w \geq -8

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(D)

w > 13

w < -8

Isolate $w$ in first inequality: First, let's solve the inequality w - 9 > 4. To isolate $w$ , we need to add $9$ to both sides of the inequality. w - 9 + 9 > 4 + 9 w > 13
Isolate $w$ in second inequality: Now, let's solve the second inequality $w + 20 \leq 12$ . To isolate $w$ , we need to subtract $20$ from both sides of the inequality. $w + 20 - 20 \leq 12 - 20$ $w \leq -8$
Combine inequalities using OR: We have two separate inequalities from the original problem: w > 13 and $w \leq -8$ . Since the original problem states ＂or＂ between the inequalities, we combine them using ＂or＂. The compound inequality is w > 13 or $w \leq -8$ .