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

Isolate absolute value: We are given the inequality -7|y| ≥ -14. The first step is to isolate the absolute value expression by dividing both sides of the inequality by -7. Remember that dividing by a negative number reverses the inequality sign. -7|y| / -7 ≤ -14 / -7 |y| ≤ 2Interpret absolute value: Now that we have |y| ≤ 2, we can interpret this as y being within the range of -2 to 2, inclusive. The absolute value inequality |y| ≤ 2 means that y can be less than or equal to 2 and greater than or equal to -2. The compound inequality is -2 ≤ y ≤ 2.

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Solve for $y$ . $\newline$ $-7|y| \geq -14$ $\newline$ 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

y

\newline

-7|y| \geq -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

______

Isolate absolute value: We are given the inequality $-7|y| \geq -14$ . The first step is to isolate the absolute value expression by dividing both sides of the inequality by $-7$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $\frac{-7|y|}{-7} \leq \frac{-14}{-7}$ $\newline$ $|y| \leq 2$
Interpret absolute value: Now that we have $|y| \leq 2$ , we can interpret this as $y$ being within the range of $-2$ to $2$ , inclusive. The absolute value inequality $|y| \leq 2$ means that $y$ can be less than or equal to $2$ and greater than or equal to $-2$ . The compound inequality is $-2 \leq y \leq 2$ .