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

Given Inequality: We have the inequality: |-8z| ≥ 8 First, we solve for |8z|. |-8z| ≥ 8 This means that the absolute value of -8z is greater than or equal to 8.Splitting Inequality: The absolute value inequality |-8z| ≥ 8 can be split into two separate inequalities because if the expression inside the absolute value is non-negative, it is equal to the expression itself, and if it is negative, it is equal to the negative of the expression. Therefore, we have: -8z ≥ 8 or -8z ≤ -8Solving First Inequality: Now we solve each inequality separately. Starting with the first one: -8z ≥ 8 Divide both sides by -8, remembering to reverse the inequality sign because we are dividing by a negative number: z ≤ -1Solving Second Inequality: Now we solve the second inequality: -8z ≤ -8 Divide both sides by -8: z ≥ 1Combining Solutions: Combining both parts of the solution, we get the compound inequality: z ≤ -1 or z ≥ 1 This is the final answer in the form of a compound inequality.

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Solve for $z$ . $\newline$ $|-8z| \geq 8$ $\newline$ $\newline$ 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. $\newline$ ______

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Algebra 2

Solve absolute value inequalities

Full solution

Q. Solve for

z

\newline

|-8z| \geq 8

\newline

\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: $\newline$ $|-8z| \geq 8$ $\newline$ First, we solve for $|8z|$ . $\newline$ $|-8z| \geq 8$ $\newline$ This means that the absolute value of $-8z$ is greater than or equal to $8$ .
Splitting Inequality: The absolute value inequality $|-8z| \geq 8$ can be split into two separate inequalities because if the expression inside the absolute value is non-negative, it is equal to the expression itself, and if it is negative, it is equal to the negative of the expression. Therefore, we have: $\newline$ $-8z \geq 8$ or $-8z \leq -8$
Solving First Inequality: Now we solve each inequality separately. Starting with the first one: $\newline$ $-8z \geq 8$ $\newline$ Divide both sides by $-8$ , remembering to reverse the inequality sign because we are dividing by a negative number: $\newline$ $z \leq -1$
Solving Second Inequality: Now we solve the second inequality: $\newline$ $-8z \leq -8$ $\newline$ Divide both sides by $-8$ : $\newline$ $z \geq 1$
Combining Solutions: Combining both parts of the solution, we get the compound inequality: $\newline$ $z \leq -1$ or $z \geq 1$ $\newline$ This is the final answer in the form of a compound inequality.