Solve for z. |z| - 8 ≤ 9 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value: We have the inequality |z| - 8 ≤ 9. To solve for |z|, we need to isolate it on one side of the inequality. |z| - 8 ≤ 9 |z| - 8 + 8 ≤ 9 + 8 |z| ≤ 17Consider absolute value definition: Now that we have |z| ≤ 17, we need to consider the definition of absolute value. The absolute value of z is less than or equal to 17, which means z is within the range of -17 to 17. This can be written as a compound inequality: -17 ≤ z ≤ 17

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Solve for $z$ . $|z| - 8 \leq 9$ 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.

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Algebra 1

Solve absolute value inequalities

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Q. Solve for

z

|z| - 8 \leq 9

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

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

Isolate absolute value: We have the inequality $|z| - 8 \leq 9$ . To solve for $|z|$ , we need to isolate it on one side of the inequality. $\newline$ $|z| - 8 \leq 9$ $\newline$ $|z| - 8 + 8 \leq 9 + 8$ $\newline$ $|z| \leq 17$
Consider absolute value definition: Now that we have $|z| \leq 17$ , we need to consider the definition of absolute value. The absolute value of $z$ is less than or equal to $17$ , which means $z$ is within the range of $-17$ to $17$ . This can be written as a compound inequality: $-17 \leq z \leq 17$