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Solve for $t$ . $|{-t}| \geq 3$ 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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Solve absolute value inequalities

Full solution

Q. Solve for

t

.

|{-t}| \geq 3

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

______

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.

More problems from Solve absolute value inequalities

Question

s

\newline

|s| + 3 \geq 8

\newline

\newline

Write a compound inequality like

1 < x < 3

x < 1

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. Use integers, proper fractions, or improper fractions in simplest form.

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x

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500+4.50M\geq5,000

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4.50+500M>5,000

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Which of the following best describes the solutions to the inequality shown?

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Question

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\newline

Which of the following best describes the solutions to the inequality shown?

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1

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x > \frac{38}{3}

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Question

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Which of the following best describes the solutions to the inequality shown?

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1

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x < \frac{3}{5}

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Question

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p

represents the selling price of the house, which equation best models the situation?

\newline

1

\newline

0.018 p-100=4580

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0.018 p+100=4580

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(100-0.018) p=4580

\newline

(100+0.018) p=4580

Posted 1 month ago

Question

A commercial airplane that is

1

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2

500

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150

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\newline

1

\newline

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1,500-600 h=2,500

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1,500-690 h=2,500

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Question

A weeping willow that is

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1

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\newline

1

\newline

35=15+2 y

\newline

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\newline

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\newline

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Question

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h

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10

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\newline

1

\newline

13-\frac{23 h}{60}=10

\newline

13-\frac{60 h}{23}=10

\newline

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\newline

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