To calculate: The solution set of the compound inequality −4≤−23p+14, graph it, and write it in set-builder notation and interval notation.

Given Information: The compound inequality, −4≤−23p+14 Calculation: The given compound inequality is −4≤−23p+14. Subtract 14 from the inequality. −4−14≤−23p+14−14 −18≤−23p Divide the inequality by −23 and change the sense of inequality, −18(−23)≥−23(−23)p After division, −18×−32≥−23×−32p 27≥p The graph of the solution is: Therefore, the solution set of compound inequality −4≤−23p+14 is {p∣p≤27} and interval notation is (−∝,27].

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High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

pavitorj6

Answered question

2021-11-21

To calculate: The solution set of the compound inequality

- 4 \leq - \frac{2}{3} p + 14

, graph it, and write it in set-builder notation and interval notation.

Answer & Explanation

navratitehf

Beginner2021-11-22Added 20 answers

Given Information:
The compound inequality,

- 4 \leq - \frac{2}{3} p + 14

Calculation:
The given compound inequality is

- 4 \leq - \frac{2}{3} p + 14

. Subtract 14 from the inequality.

- 4 - 14 \leq - \frac{2}{3} p + 14 - 14

- 18 \leq - \frac{2}{3} p

Divide the inequality by

- \frac{2}{3}

and change the sense of inequality,

\frac{- 18}{(- \frac{2}{3})} \geq \frac{- \frac{2}{3}}{(- \frac{2}{3})} p

After division,

- 18 \times - \frac{3}{2} \geq - \frac{2}{3} \times - \frac{3}{2} p

27 \geq p

The graph of the solution is:

Therefore, the solution set of compound inequality

- 4 \leq - \frac{2}{3} p + 14

{p ∣ p \leq 27}

and interval notation is

(- \propto, 27]

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