Solve for z. |-2z| ≤ 8 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Inequality Analysis: We have the inequality: |-2z| ≤ 8 First, we solve for |-2z|. |-2z| ≤ 8 This means that -2z is less than or equal to 8 and greater than or equal to -8.Splitting Inequality: Now we split the inequality into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. -2z ≤ 8 and -2z ≥ -8Solving First Inequality: We solve the first inequality for z: -2z ≤ 8 Divide both sides by -2, remembering to reverse the inequality sign because we are dividing by a negative number. z ≥ -4Solving Second Inequality: We solve the second inequality for z: -2z ≥ -8 Divide both sides by -2, again reversing the inequality sign. z ≤ 4Combining Inequalities: Now we combine both inequalities to get the compound inequality: -4 ≤ z ≤ 4 This is the solution to the inequality |-2z| ≤ 8.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $z$ . $|{-2z}| \leq 8$ 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.______

View step-by-step help

Home

Math Problems

Algebra 2

Solve absolute value inequalities

Full solution

Q. Solve for

z

|{-2z}| \leq 8

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

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

Inequality Analysis: We have the inequality: $\newline$ $|-2z| \leq 8$ $\newline$ First, we solve for $|-2z|$ . $\newline$ $|-2z| \leq 8$ $\newline$ This means that $-2z$ is less than or equal to $8$ and greater than or equal to $-8$ .
Splitting Inequality: Now we split the inequality into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. $\newline$ $-2z \leq 8$ and $-2z \geq -8$
Solving First Inequality: We solve the first inequality for $z$ : $-2z \leq 8$ Divide both sides by $-2$ , remembering to reverse the inequality sign because we are dividing by a negative number. $z \geq -4$
Solving Second Inequality: We solve the second inequality for $z$ : $-2z \geq -8$ Divide both sides by $-2$ , again reversing the inequality sign. $z \leq 4$
Combining Inequalities: Now we combine both inequalities to get the compound inequality: $\newline$ $-4 \leq z \leq 4$ $\newline$ This is the solution to the inequality $|-2z| \leq 8$ .