Solve for u. |-u| > 14 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Understand absolute value: We have the inequality: |-u| > 14 First, we need to understand the absolute value inequality. The absolute value of a number is always non-negative, so |-u| > 14 means that the value of -u is either greater than 14 or less than -14.Split into two inequalities: Now we can split the inequality into two separate inequalities to remove the absolute value: -u > 14 or -u 14 Multiply both sides by -1 (remember to flip the inequality sign when multiplying or dividing by a negative number): u 14Combine both inequalities: Combining both inequalities, we get the compound inequality: u 14 This is the solution to the original problem.

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Solve for $u$ . $\newline$ |-u| > 14 $\newline$ 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 1

Solve absolute value inequalities

Full solution

Q. Solve for

u

\newline

|-u| > 14

\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

______

Understand absolute value: We have the inequality: $\newline$ |-u| > 14 $\newline$ First, we need to understand the absolute value inequality. The absolute value of a number is always non-negative, so |-u| > 14 means that the value of $-u$ is either greater than $14$ or less than $-14$ .
Split into two inequalities: Now we can split the inequality into two separate inequalities to remove the absolute value: -u > 14 or -u < -14
Solve first inequality: Next, we solve each inequality for $u$ . Starting with the first inequality: -u > 14 Multiply both sides by $-1$ (remember to flip the inequality sign when multiplying or dividing by a negative number): u < -14
Solve second inequality: Now, we solve the second inequality: $\newline$ -u < -14 $\newline$ Multiply both sides by $-1$ (again, remember to flip the inequality sign): $\newline$ u > 14
Combine both inequalities: Combining both inequalities, we get the compound inequality: $\newline$ u < -14 or u > 14 $\newline$ This is the solution to the original problem.