Solve for d. -7|d| > -14 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Divide and Reverse Inequality: We have the inequality: -7|d| > -14 First, we divide both sides of the inequality by -7 to isolate |d|. Remember that dividing by a negative number reverses the inequality sign. -7|d| / -7 < -14 / -7 |d| < 2Interpret Absolute Value Inequality: Now we interpret the absolute value inequality |d| < 2. This means that d is less than 2 units away from 0 on the number line, so d can be between -2 and 2, but not including -2 and 2 since the inequality is strict (not ≤ or ≥). So, the compound inequality is: -2 < d < 2

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Solve for $d$ . $\newline$ -7|d| > -14 $\newline$ 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 1

Solve absolute value inequalities

Full solution

Q. Solve for

d

\newline

-7|d| > -14

\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

______

Divide and Reverse Inequality: We have the inequality: $\newline$ -7|d| > -14 $\newline$ First, we divide both sides of the inequality by $-7$ to isolate $|d|$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ -7|d| / -7 < -14 / -7 $\newline$ |d| < 2
Interpret Absolute Value Inequality: Now we interpret the absolute value inequality |d| < 2. This means that $d$ is less than $2$ units away from $0$ on the number line, so $d$ can be between $-2$ and $2$ , but not including $-2$ and $2$ since the inequality is strict (not $\leq$ or $d$ $0$ ). $\newline$ So, the compound inequality is: $\newline$ $d$ $1$