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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

u

\newline

|u| - 4 \geq 6

\newline

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

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

\newline

Posted 3 months ago

Question

9 \frac{7}{8}

into an improper fraction.

\newline

Posted 2 months ago

Question

f(x)=\left\{\begin{array}{lll} -4 x & \text { for } & x<-1 \\ -x+1 & \text { for } & -1 \leq x \leq 3 \\ -2 x+8 & \text { for } & x>3 \end{array}\right.

\newline

f(3)

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Solve the system of equations.

\newline

\begin{array}{l}y=22 x-38 \\y=x^{2}+11 x-14\end{array}

\newline

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\newline

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Question

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\newline

\frac{2}{5}

\newline

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\newline

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Question

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\newline

The probability that the three-digit number is even and greater than

600

\square

\newline

(Type an integer or a simplified fraction.)

Posted 2 months ago

Question

Use benchmark fractions to estimate sums and differences less than or gremet than

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\newline

\begin{array}{l} \frac{7}{8}+\frac{5}{10} \\ 1 \frac{5}{8}-\frac{5}{6} \\ \frac{10}{10}-\frac{2}{3} \\ \frac{1}{2}+\frac{2}{3} \\ \frac{5}{12}+\frac{1}{4} \\ 1 \frac{1}{6}+\frac{7}{8} \\ \end{array}

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Question

Eric is sorting pencils into boxes. He put

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pencils in the fourth box. What kind of sequence is this?

\newline

\newline

\newline

\newline

\newline

Posted 2 months ago

Question

Given the definitions of

f(x)

g(x)

below, find the value of

g(f(2))

\newline

\begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array}

\newline

Posted 2 months ago

Question

t

\newline

|t + 8| \leq 4

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

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

\newline

Posted 2 months ago