Solve for z. |-2z| ≤ 18 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Given Inequality: We are given the inequality: |-2z| ≤ 18 First, we need to solve for |2z|. |-2z| ≤ 18 This means that the absolute value of -2z is less than or equal to 18.Split Absolute Value: The absolute value inequality |-2z| ≤ 18 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. Therefore, we have: -2z ≤ 18 and -2z ≥ -18Solve First Inequality: Now we solve each inequality for z. Starting with the first inequality: -2z ≤ 18 Divide both sides by -2 to isolate z. Remember that dividing by a negative number reverses the inequality sign. z ≥ -9Solve Second Inequality: Now we solve the second inequality: -2z ≥ -18 Divide both sides by -2, again remembering to reverse the inequality sign. z ≤ 9Combine Inequalities: Combining both inequalities, we get the compound inequality: -9 ≤ z ≤ 9 This is the solution to the original problem.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $z$ . $\newline$ $|-2z| \leq 18$ $\newline$ 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

z

\newline

|-2z| \leq 18

\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 are given the inequality: $\newline$ $|-2z| \leq 18$ $\newline$ First, we need to solve for $|2z|$ . $\newline$ $|-2z| \leq 18$ $\newline$ This means that the absolute value of $-2z$ is less than or equal to $18$ .
Split Absolute Value: The absolute value inequality $|-2z| \leq 18$ 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. Therefore, we have: $\newline$ $-2z \leq 18$ and $-2z \geq -18$
Solve First Inequality: Now we solve each inequality for $z$ . Starting with the first inequality: $\newline$ $-2z \leq 18$ $\newline$ Divide both sides by $-2$ to isolate $z$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $z \geq -9$
Solve Second Inequality: Now we solve the second inequality: $\newline$ $-2z \geq -18$ $\newline$ Divide both sides by $-2$ , again remembering to reverse the inequality sign. $\newline$ $z \leq 9$
Combine Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-9 \leq z \leq 9$ $\newline$ This is the solution to the original problem.