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

Understand absolute value inequality: We have the inequality: |-r| ≤ 7 First, we need to understand the absolute value inequality. The absolute value of a number is the distance of that number from 0 on the number line, regardless of direction. Therefore, |-r| ≤ 7 means that the value of -r is within 7 units of 0 on the number line.Split into two inequalities: Since the absolute value of -r is less than or equal to 7, we can split this into two separate inequalities: -r ≤ 7 and -r ≥ -7Solve first inequality: Now we solve each inequality for r. Starting with the first inequality: -r ≤ 7 Multiply both sides by -1 (remember to flip the inequality sign when multiplying or dividing by a negative number): r ≥ -7Solve second inequality: Next, we solve the second inequality: -r ≥ -7 Multiply both sides by -1 (again, flip the inequality sign): r ≤ 7Combine both inequalities: Combining both inequalities, we get the compound inequality: -7 ≤ r ≤ 7 This means that r can be any number between -7 and 7, inclusive.

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Solve for $r$ . $\newline$ $|-r| \leq 7$ $\newline$ $\newline$ 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

r

\newline

|-r| \leq 7

\newline

\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

______

Understand absolute value inequality: We have the inequality: $\newline$ $|-r| \leq 7$ $\newline$ First, we need to understand the absolute value inequality. The absolute value of a number is the distance of that number from $0$ on the number line, regardless of direction. Therefore, $|-r| \leq 7$ means that the value of $-r$ is within $7$ units of $0$ on the number line.
Split into two inequalities: Since the absolute value of $-r$ is less than or equal to $7$ , we can split this into two separate inequalities: $\newline$ $-r \leq 7$ and $-r \geq -7$
Solve first inequality: Now we solve each inequality for $r$ . Starting with the first inequality: $-r \leq 7$ Multiply both sides by $-1$ (remember to flip the inequality sign when multiplying or dividing by a negative number): $r \geq -7$
Solve second inequality: Next, we solve the second inequality: $-r \geq -7$ Multiply both sides by $-1$ (again, flip the inequality sign): $r \leq 7$
Combine both inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-7 \leq r \leq 7$ $\newline$ This means that $r$ can be any number between $-7$ and $7$ , inclusive.