Question

solve for r.\
-7|r| + 6 < -1\
write a compound inequality like 1 < x < 3 or like x < 1 or x >\
fractions, or improper fractions in simplest form.

Explanation:

Step1: Isolate the absolute value term

Subtract 6 from both sides of the inequality:
$-7|r| + 6 - 6 < -1 - 6$
Simplify to get:
$-7|r| < -7$

Step2: Divide both sides by -7 (and reverse the inequality sign)

When dividing an inequality by a negative number, the direction of the inequality sign changes. So we have:
$\frac{-7|r|}{-7} > \frac{-7}{-7}$
Simplify to:
$|r| > 1$

Step3: Solve the absolute value inequality

The absolute value inequality $|r| > 1$ means that $r$ is either less than -1 or greater than 1. This is because the absolute value of a number represents its distance from 0 on the number line, so if the distance is greater than 1, the number is either to the left of -1 (less than -1) or to the right of 1 (greater than 1).

Answer:

$r < -1$ or $r > 1$