Question

solve for q.
-3(q + 15) - 14 < -5

Explanation:

Step1: Expand the left - hand side

First, expand $-3(q + 15)$ using the distributive property $a(b + c)=ab+ac$. Here $a=-3$, $b = q$, $c = 15$. So $-3(q + 15)=-3q-45$. The inequality becomes $-3q-45-14\lt - 5$.

Step2: Combine like terms

Combine the constant terms on the left - hand side: $-45-14=-59$. The inequality is now $-3q-59\lt - 5$.

Step3: Isolate the term with $q$

Add 59 to both sides of the inequality: $-3q-59 + 59\lt-5 + 59$, which simplifies to $-3q\lt54$.

Step4: Solve for $q$

Divide both sides of the inequality by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $\frac{-3q}{-3}>\frac{54}{-3}$, which gives $q>-18$.

Answer:

$q > - 18$