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Solve for $t$ . $\newline$ -|t| < -8 $\newline$ 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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Solve absolute value inequalities

Full solution

Q. Solve for

t

.

\newline

-|t| < -8

\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

______

Isolate absolute value: We are given the inequality -|t| < -8. To solve for $t$ , we first need to isolate the absolute value expression on one side of the inequality. Since the absolute value is being multiplied by $-1$ , we can divide both sides of the inequality by $-1$ to get |t| > 8. Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the direction of the inequality. $\newline$ Calculation: -|t| < -8 \rightarrow |t| > 8 (after dividing by $-1$ and reversing the inequality)
Interpret absolute value: Now that we have |t| > 8, we can interpret this as $t$ being greater than $8$ or less than $-8$ . This is because the absolute value of $t$ is greater than $8$ , which means $t$ is more than $8$ units away from $0$ on the number line, in either direction. $\newline$ Compound inequality: t > 8 or $t$ $0$

More problems from Solve absolute value inequalities

Question

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Write a compound inequality like

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

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Question

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Question

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\newline

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Question

t

\newline

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Question

p

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

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Question

v

\newline

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\newline

Write a compound inequality like

1 < x < 3

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

\newline

Posted 8 months ago

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