Solve for u. |-4u| ≥ 20 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Given Inequality: We have the inequality: |-4u| ≥ 20 First, we solve for |-4u|. |-4u| ≥ 20 means that the absolute value of -4u is greater than or equal to 20.Split into Two Inequalities: The absolute value inequality |-4u| ≥ 20 can be split into two separate inequalities: -4u ≥ 20 or -4u ≤ -20 This is because the absolute value of a number is the distance from zero, so it can be either positive or negative.Solve First Inequality: Solve the first inequality -4u ≥ 20. Divide both sides by -4 to isolate u. Remember that dividing by a negative number reverses the inequality sign. -4u / -4 ≤ 20 / -4 u ≤ -5Solve Second Inequality: Solve the second inequality -4u ≤ -20. Divide both sides by -4 to isolate u. Again, remember that dividing by a negative number reverses the inequality sign. -4u / -4 ≥ -20 / -4 u ≥ 5Combine Results: Combine the results from Step 3 and Step 4 to write the compound inequality. The compound inequality is: u ≤ -5 or u ≥ 5

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Solve for $u$ . $\newline$ $|-4u| \geq 20$ $\newline$ $\newline$ 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. $\newline$ ______ $\newline$

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Math Problems

Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

u

\newline

|-4u| \geq 20

\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

______

\newline

Given Inequality: We have the inequality: $\newline$ $|-4u| \geq 20$ $\newline$ First, we solve for $|-4u|$ . $\newline$ $|-4u| \geq 20$ means that the absolute value of $-4u$ is greater than or equal to $20$ .
Split into Two Inequalities: The absolute value inequality $|-4u| \geq 20$ can be split into two separate inequalities: $\newline$ $-4u \geq 20$ or $-4u \leq -20$ $\newline$ This is because the absolute value of a number is the distance from zero, so it can be either positive or negative.
Solve First Inequality: Solve the first inequality $-4u \geq 20$ . $\newline$ Divide both sides by $-4$ to isolate $u$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $-4u / -4 \leq 20 / -4$ $\newline$ $u \leq -5$
Solve Second Inequality: Solve the second inequality $-4u \leq -20$ . $\newline$ Divide both sides by $-4$ to isolate $u$ . Again, remember that dividing by a negative number reverses the inequality sign. $\newline$ $-4u / -4 \geq -20 / -4$ $\newline$ $u \geq 5$
Combine Results: Combine the results from Step $3$ and Step $4$ to write the compound inequality. $\newline$ The compound inequality is: $\newline$ $u \leq -5$ or $u \geq 5$