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Solve for $q$ . $\newline$ $1 < \frac{q - 15}{-18}$

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Solve advanced linear inequalities

Full solution

Q. Solve for

q

.

\newline

1 < \frac{q - 15}{-18}

Multiply to Simplify: First, we need to simplify the inequality by multiplying both sides by $-18$ to get rid of the fraction. Remember that multiplying by a negative number will reverse the inequality sign. $\newline$ $1 < \frac{q - 15}{-18}$ $\newline$ $-18 \times 1 < -18 \times \left(q - \frac{15}{-18}\right)$
Perform Multiplication: Perform the multiplication on the left side of the inequality. $\newline$ $-18 < -18 \times (q - \frac{15}{-18})$ $\newline$ $-18 < -18q + 15$
Isolate Variable $q$ : Now, we isolate the variable $q$ by adding $18q$ to both sides of the inequality. $\newline$ $-18 + 18q < -18q + 18q + 15$ $\newline$ $18q - 18 < 15$
Add to Isolate $q$ : Next, we add $18$ to both sides of the inequality to further isolate $q$ . $\newline$ $18q - 18 + 18 < 15 + 18$ $\newline$ $18q < 33$
Divide to Solve $q$ : Finally, we divide both sides of the inequality by $18$ to solve for $q$ . $\frac{18q}{18} < \frac{33}{18}$ $q < \frac{33}{18}$
Simplify Fraction: Simplify the fraction on the right side of the inequality. $q < \frac{11}{6}$

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