Solve for p. 7 ≤ p + 18 ≤ 15 Write your answer as a compound inequality with integers. Choices: (A)-11 ≤ p ≤ -3 (B)25 ≤ p ≤ 33 (C)-11 ≤ p ≤ 33 (D)25 ≤ p ≤ -3

Isolate p: To isolate p, we need to subtract 18 from all parts of the inequality because p + 18 involves addition of 18 to p.Subtract 18: Subtract 18 from all parts of the inequality: 7 ≤ p + 18 ≤ 15 7 - 18 ≤ p + 18 - 18 ≤ 15 - 18 -11 ≤ p ≤ -3Check Solution: Check the solution by substituting the boundary values for p into the original inequality to ensure they satisfy the conditions: For p = -11: 7 ≤ -11 + 18 ≤ 15 which simplifies to 7 ≤ 7 ≤ 15, which is true. For p = -3: 7 ≤ -3 + 18 ≤ 15 which simplifies to 7 ≤ 15 ≤ 15, which is also true.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

p

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7 \leq p + 18 \leq 15

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

-11 \leq p \leq -3

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(B)

25 \leq p \leq 33

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(C)

-11 \leq p \leq 33

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(D)

25 \leq p \leq -3

Isolate $p$ : To isolate $p$ , we need to subtract $18$ from all parts of the inequality because $p + 18$ involves addition of $18$ to $p$ .
Subtract $18$ : Subtract $18$ from all parts of the inequality: $\newline$ $7 \leq p + 18 \leq 15$ $\newline$ $7 - 18 \leq p + 18 - 18 \leq 15 - 18$ $\newline$ $-11 \leq p \leq -3$
Check Solution: Check the solution by substituting the boundary values for $p$ into the original inequality to ensure they satisfy the conditions: $\newline$ For $p = -11$ : $7 \leq -11 + 18 \leq 15$ which simplifies to $7 \leq 7 \leq 15$ , which is true. $\newline$ For $p = -3$ : $7 \leq -3 + 18 \leq 15$ which simplifies to $7 \leq 15 \leq 15$ , which is also true.