Solve for u. |-7u| ≤ 7 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Identify Inequality: We have the inequality: |-7u| ≤ 7 First, we solve for |-7u|. |-7u| ≤ 7 This means that -7u is less than or equal to 7 and greater than or equal to -7.Split into Two: 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. -7u ≤ 7 and -7u ≥ -7Solve for -7u: We solve the first inequality for u: -7u ≤ 7 To isolate u, we divide both sides by -7. Remember that dividing by a negative number reverses the inequality sign. u ≥ -1Combine Inequalities: We solve the second inequality for u: -7u ≥ -7 Again, we divide both sides by -7, and the inequality sign reverses. u ≤ 1Final Compound Inequality: Now we combine both inequalities to form the compound inequality: -1 ≤ u ≤ 1 This is the solution to the given problem.

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Solve for $u$ . $\newline$ $|-7u| \leq 7$ $\newline$ 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

|-7u| \leq 7

\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

______

Identify Inequality: We have the inequality: $\newline$ $|-7u| \leq 7$ $\newline$ First, we solve for $|-7u|$ . $\newline$ $|-7u| \leq 7$ $\newline$ This means that $-7u$ is less than or equal to $7$ and greater than or equal to $-7$ .
Split into Two: 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. $\newline$ $-7u \leq 7$ and $-7u \geq -7$
Solve for $-7u$ : We solve the first inequality for $u$ : $-7u \leq 7$ To isolate $u$ , we divide both sides by $-7$ . Remember that dividing by a negative number reverses the inequality sign. $u \geq -1$
Combine Inequalities: We solve the second inequality for $u$ : $\newline$ $-7u \geq -7$ $\newline$ Again, we divide both sides by $-7$ , and the inequality sign reverses. $\newline$ $u \leq 1$
Final Compound Inequality: Now we combine both inequalities to form the compound inequality: $-1 \leq u \leq 1$ This is the solution to the given problem.