Solve for p. |-5p| ≤ 10 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Given Inequality: We have the inequality: |-5p| ≤ 10 First, we need to solve for |-5p|. |-5p| ≤ 10 means that the absolute value of -5p is less than or equal to 10.Splitting Inequality: The absolute value inequality |-5p| ≤ 10 can be split into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. So we have: -5p ≤ 10 and -5p ≥ -10Solving First Inequality: Now we solve each inequality for p. Starting with the first inequality: -5p ≤ 10 To isolate p, we divide both sides by -5. Remember that dividing by a negative number reverses the inequality sign: p ≥ -2Solving Second Inequality: Next, we solve the second inequality: -5p ≥ -10 Again, we divide both sides by -5, and reverse the inequality sign: p ≤ 2Combining Inequalities: Combining both inequalities, we get the compound inequality: -2 ≤ p ≤ 2 This is the solution to the given problem.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $p$ . $\newline$ $|-5p| \leq 10$ $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

View step-by-step help

Home

Math Problems

Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

p

\newline

|-5p| \leq 10

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Given Inequality: We have the inequality: $\newline$ $|-5p| \leq 10$ $\newline$ First, we need to solve for $|-5p|$ . $\newline$ $|-5p| \leq 10$ means that the absolute value of $-5p$ is less than or equal to $10$ .
Splitting Inequality: The absolute value inequality $|-5p| \leq 10$ can be split into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. So we have: $\newline$ $-5p \leq 10$ and $-5p \geq -10$
Solving First Inequality: Now we solve each inequality for $p$ . Starting with the first inequality: $\newline$ $-5p \leq 10$ $\newline$ To isolate $p$ , we divide both sides by $-5$ . Remember that dividing by a negative number reverses the inequality sign: $\newline$ $p \geq -2$
Solving Second Inequality: Next, we solve the second inequality: $\newline$ $-5p \geq -10$ $\newline$ Again, we divide both sides by $-5$ , and reverse the inequality sign: $\newline$ $p \leq 2$
Combining Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-2 \leq p \leq 2$ $\newline$ This is the solution to the given problem.