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

Divide by 4: We are given the inequality |4t| ≥ 4 and we need to solve for t. First, we divide both sides of the inequality by 4 to isolate the absolute value of t. |4t| ≥ 4 |4t|/4 ≥ 4/4 |t| ≥ 1Consider Two Cases: Now we have |t| ≥ 1. The absolute value inequality |t| ≥ 1 means that t is at a distance of at least 1 from 0 on the number line. This gives us two cases to consider: 1. t ≥ 1 (when t is positive or zero) 2. t ≤ -1 (when t is negative)Write Compound Inequality: We can now write the compound inequality that represents the solution to the original inequality |4t| ≥ 4. The compound inequality is t ≥ 1 or t ≤ -1.

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Solve for $t$ . $\newline$ $|4t| \geq 4$ $\newline$ 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

t

\newline

|4t| \geq 4

\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

______

Divide by $4$ : We are given the inequality $|4t| \geq 4$ and we need to solve for $t$ . First, we divide both sides of the inequality by $4$ to isolate the absolute value of $t$ . $|4t| \geq 4$ $|4t|/4 \geq 4/4$ $|t| \geq 1$
Consider Two Cases: Now we have $|t| \geq 1$ . The absolute value inequality $|t| \geq 1$ means that $t$ is at a distance of at least $1$ from $0$ on the number line. $\newline$ This gives us two cases to consider: $\newline$ $1$ . $t \geq 1$ (when $t$ is positive or zero) $\newline$ $2$ . $t \leq -1$ (when $t$ is negative)
Write Compound Inequality: We can now write the compound inequality that represents the solution to the original inequality $|4t| \geq 4$ . The compound inequality is $t \geq 1$ or $t \leq -1$ .