Solve for r. -1(r - 13) ≥ 3 ______

Distribute -1: Distribute -1 across the parentheses in the inequality -1(r - 13) ≥ 3. -1 * r + -1 * (-13) ≥ 3 -r + 13 ≥ 3Isolate variable term: Isolate the variable term by subtracting 13 from both sides of the inequality. -r + 13 - 13 ≥ 3 - 13 -r ≥ -10Divide by -1: Divide both sides by -1 to solve for r. Remember that dividing by a negative number reverses the inequality sign. -r / -1 ≤ -10 / -1 r ≤ 10Check solution: Check the solution by substituting the value back into the original inequality to ensure it makes the inequality true. -1(10 - 13) ≥ 3 -1(-3) ≥ 3 3 ≥ 3 This is true, so there is no math error.

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Math Problems

Algebra 1

Solve advanced linear inequalities

Full solution

Q. Solve for

r

\newline

-1(r - 13) \geq 3

Distribute $-1$ : Distribute $-1$ across the parentheses in the inequality $-1(r - 13) \geq 3$ .
$-1 \times r + -1 \times (-13) \geq 3$
$-r + 13 \geq 3$
Isolate variable term: Isolate the variable term by subtracting $13$ from both sides of the inequality. $\newline$ $-r + 13 - 13 \geq 3 - 13$ $\newline$ $-r \geq -10$
Divide by $-1$ : Divide both sides by $-1$ to solve for $r$ . Remember that dividing by a negative number reverses the inequality sign. $\frac{-r}{-1} \leq \frac{-10}{-1}$ $r \leq 10$
Check solution: Check the solution by substituting the value back into the original inequality to ensure it makes the inequality true. $\newline$ $-1(10 - 13) \geq 3$ $\newline$ $-1(-3) \geq 3$ $\newline$ $3 \geq 3$ $\newline$ This is true, so there is no math error.