Solve for u. |u| – 4 ≥ 6 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Isolate absolute value expression: We are given the inequality |u| – 4 ≥ 6. Our first step is to isolate the absolute value expression on one side of the inequality. |u| - 4 + 4 ≥ 6 + 4 Simplifying both sides gives us: |u| ≥ 10Consider definition of absolute value: Now that we have |u| ≥ 10, we need to consider the definition of absolute value. The absolute value of u is greater than or equal to 10 means that u is either greater than or equal to 10 or less than or equal to -10. This gives us two inequalities: u ≥ 10 or u ≤ -10Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality. The compound inequality is: u ≤ -10 or u ≥ 10

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Solve for $u$ . $\newline$ $|u| - 4 \geq 6$ $\newline$ $\newline$ 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. $\newline$ ________

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Math Problems

Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

u

\newline

|u| - 4 \geq 6

\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

________

Isolate absolute value expression: We are given the inequality $|u| - 4 \geq 6$ . Our first step is to isolate the absolute value expression on one side of the inequality. $\newline$ $|u| - 4 + 4 \geq 6 + 4$ $\newline$ Simplifying both sides gives us: $\newline$ $|u| \geq 10$
Consider definition of absolute value: Now that we have $|u| \geq 10$ , we need to consider the definition of absolute value. The absolute value of $u$ is greater than or equal to $10$ means that $u$ is either greater than or equal to $10$ or less than or equal to $-10$ . $\newline$ This gives us two inequalities: $\newline$ $u \geq 10$ or $u \leq -10$
Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality. $\newline$ The compound inequality is: $\newline$ $u \leq -10$ or $u \geq 10$