Question

solve for b.
\\(\frac{b}{-19} + 13 \leq 14\\)

Explanation:

Step1: Subtract 13 from both sides

To isolate the term with \( b \), we subtract 13 from both sides of the inequality \(\frac{b}{-19}+13\leq14\).

$$ \frac{b}{-19}+13 - 13\leq14 - 13 $$

Simplifying both sides, we get:

$$ \frac{b}{-19}\leq1 $$

Step2: Multiply both sides by -19 (and reverse inequality)

When we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign. So we multiply both sides of \(\frac{b}{-19}\leq1\) by -19.

$$ \frac{b}{-19}\times(-19)\geq1\times(-19) $$

Simplifying both sides, we find:

$$ b\geq - 19 $$

Answer:

\(b \geq -19\)