Question

solve for d.
-19d - 37 ≥ -29 + 35d or d - 10 > 65
write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Solve the first - inequality

Starting with \(-19d - 37\geq - 29+35d\). Add \(19d\) to both sides: \(-37\geq - 29 + 35d+19d\), which simplifies to \(-37\geq - 29+54d\). Then add \(29\) to both sides: \(-37 + 29\geq54d\), so \(-8\geq54d\). Divide both sides by \(54\): \(d\leq-\frac{8}{54}=-\frac{4}{27}\).

Step2: Solve the second - inequality

Starting with \(d - 10>65\). Add \(10\) to both sides: \(d>65 + 10\), so \(d>75\).

Answer:

\(d\leq-\frac{4}{27}\) or \(d>75\)