Solve for d. |-d| > 10 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Given Inequality: We have the inequality: |-d| > 10 Solve for |-d|. |-d| > 10 Since the absolute value of a number is always non-negative, the inequality |-d| > 10 means that the value inside the absolute value must be either greater than 10 or less than -10.Absolute Value: |-d| > 10 is equivalent to two separate inequalities because the absolute value of a number is the distance from zero, and it can be on either side of the number line. So, we have: -d > 10 or -d 10 Multiply both sides by -1 (remember to reverse the inequality sign when multiplying or dividing by a negative number): d 10Second Inequality: Combine the two inequalities to form the compound inequality: d 10 This is the solution to the original problem.

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Solve for $d$ . $\newline$ |-d| > 10 $\newline$ 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

d

\newline

|-d| > 10

\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

______

Given Inequality: We have the inequality: $\newline$ |-d| > 10 $\newline$ Solve for $|-d|$ . $\newline$ |-d| > 10 $\newline$ Since the absolute value of a number is always non-negative, the inequality |-d| > 10 means that the value inside the absolute value must be either greater than $10$ or less than $-10$ .
Absolute Value: |-d| > 10 is equivalent to two separate inequalities because the absolute value of a number is the distance from zero, and it can be on either side of the number line. $\newline$ So, we have: $\newline$ -d > 10 or -d < -10
Solve for $d$ : Now, we solve each inequality for $d$ .
First inequality:
-d > 10
Multiply both sides by $-1$ (remember to reverse the inequality sign when multiplying or dividing by a negative number):
d < -10
First Inequality: Second inequality: $\newline$ -d < -10 $\newline$ Multiply both sides by $-1$ (again, reverse the inequality sign): $\newline$ d > 10
Second Inequality: Combine the two inequalities to form the compound inequality: $\newline$ d < -10 or d > 10 $\newline$ This is the solution to the original problem.