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Solve for $d$ . $\newline$ $|-3d| > 9$ $\newline$ 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

d

.

\newline

|-3d| > 9

\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

______

Given Inequality: We have the inequality: $\newline$ $|-3d| > 9$ $\newline$ First, we solve for $|-3d|$ . $\newline$ $|-3d| > 9$ $\newline$ This means that either $-3d > 9$ or $3d > 9$ , because the absolute value of a number is greater than $9$ if the number itself is either greater than $9$ or less than $-9$ .
Solving for $|-3d|$ : Now we solve the first part of the inequality: $\newline$ $-3d > 9$ $\newline$ To isolate $d$ , we divide both sides by $-3$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $\frac{-3d}{-3} < \frac{9}{-3}$ $\newline$ $d < -3$
Solving $-3d > 9$ : Next, we solve the second part of the inequality: $\newline$ $3d > 9$ $\newline$ Again, we isolate $d$ by dividing both sides by $3$ . $\newline$ $\frac{3d}{3} > \frac{9}{3}$ $\newline$ $d > 3$
Solving $3d > 9$ : Combining both parts of the inequality, we get the compound inequality: $\newline$ $d < -3$ or $d > 3$ $\newline$ This is the solution to the inequality $|-3d| > 9$ .

More problems from Solve absolute value inequalities

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\newline

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

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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

1

\newline

0.018 p-100=4580

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0.018 p+100=4580

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1,500-600 h=2,500

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1

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\newline

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\newline

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Question

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\newline

1

\newline

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