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

Given Inequality: We have the inequality: |-8u| ≥ 8 First, we solve for |-8u|. |-8u| ≥ 8 This means that -8u is either greater than or equal to 8 or less than or equal to -8, because the absolute value of a number is the distance from zero, which is always non-negative.Solve for |-8u|: Now we split the inequality into two cases, one for each possible sign of -8u. Case 1: -8u ≥ 8 Case 2: -8u ≤ -8Split into Cases: Let's solve Case 1: -8u ≥ 8 To isolate u, we divide both sides by -8. Remember that dividing by a negative number reverses the inequality sign. u ≤ -1Case 1 Solution: Now let's solve Case 2: -8u ≤ -8 Again, we divide both sides by -8, which reverses the inequality sign. u ≥ 1Case 2 Solution: Combining both cases, we get the compound inequality: u ≤ -1 or u ≥ 1 This is the solution to the inequality |-8u| ≥ 8.

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Solve for $u$ . $\newline$ $|-8u| \geq 8$ $\newline$ 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

u

\newline

|-8u| \geq 8

\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: $\newline$ $|-8u| \geq 8$ $\newline$ First, we solve for $|-8u|$ . $\newline$ $|-8u| \geq 8$ $\newline$ This means that $-8u$ is either greater than or equal to $8$ or less than or equal to $-8$ , because the absolute value of a number is the distance from zero, which is always non-negative.
Solve for $|-8u|$ : Now we split the inequality into two cases, one for each possible sign of $-8u$ .
Case $1$ : $-8u \geq 8$
Case $2$ : $-8u \leq -8$
Split into Cases: Let's solve Case $1$ : $\newline$ $-8u \geq 8$ $\newline$ To isolate $u$ , we divide both sides by $-8$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $u \leq -1$
Case $1$ Solution: Now let's solve Case $2$ : $\newline$ $-8u \leq -8$ $\newline$ Again, we divide both sides by $-8$ , which reverses the inequality sign. $\newline$ $u \geq 1$
Case $2$ Solution: Combining both cases, we get the compound inequality: $\newline$ $u \leq -1$ or $u \geq 1$ $\newline$ This is the solution to the inequality $|-8u| \geq 8$ .