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

Absolute Value of -t: We have the inequality: |-t| ≥ 3 First, we solve for |-t|. |-t| is the absolute value of -t, which means it is the distance of -t from 0 on the number line. The absolute value of a number is always non-negative, so |-t| can be either t or -t, depending on the sign of t.Splitting into Two Inequalities: Since |-t| represents the distance from 0, it can be split into two separate inequalities: -t ≥ 3 or t ≥ 3 However, since we have -t in the first inequality, we need to multiply both sides by -1 to solve for t. Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.Solving for t: Multiplying the first inequality by -1 gives us: t ≤ -3 So now we have two inequalities: t ≤ -3 or t ≥ 3 This is the compound inequality that represents the solution to the original problem.

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Solve for $t$ . $\newline$ $|{-t}| \geq 3$

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Algebra 2

Solve absolute value inequalities

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Q. Solve for

t

\newline

|{-t}| \geq 3

Absolute Value of $-t$ : We have the inequality: $\newline$ $|-t| \geq 3$ $\newline$ First, we solve for $|-t|$ . $\newline$ $|-t|$ is the absolute value of $-t$ , which means it is the distance of $-t$ from $0$ on the number line. The absolute value of a number is always non-negative, so $|-t|$ can be either $t$ or $-t$ , depending on the sign of $t$ .
Splitting into Two Inequalities: Since $|-t| ) represents the distance from \$0$ , it can be split into two separate inequalities: $\newline$ $-t \geq 3$ or $t \geq 3$ $\newline$ However, since we have $-t$ in the first inequality, we need to multiply both sides by $-1$ to solve for $t$ . Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.
Solving for t: Multiplying the first inequality by $-1$ gives us: $\newline$ $t \leq -3$ $\newline$ So now we have two inequalities: $\newline$ $t \leq -3$ or $t \geq 3$ $\newline$ This is the compound inequality that represents the solution to the original problem.