Question

linear inequalities (level 1)
question
solve the following inequality for q. write your answer in simplest form.
8q + 5 ≤ 4q + 10

Explanation:

Step1: Subtract 4q from both sides

To isolate the variable terms, we subtract \(4q\) from both sides of the inequality \(8q + 5 \leq 4q + 10\). This gives us \(8q - 4q + 5 \leq 4q - 4q + 10\), which simplifies to \(4q + 5 \leq 10\).

Step2: Subtract 5 from both sides

Next, we subtract 5 from both sides to isolate the term with \(q\). So, \(4q + 5 - 5 \leq 10 - 5\), which simplifies to \(4q \leq 5\).

Step3: Divide both sides by 4

Finally, we divide both sides by 4 to solve for \(q\). This gives us \(\frac{4q}{4} \leq \frac{5}{4}\), so \(q \leq \frac{5}{4}\).

Answer:

\(q \leq \frac{5}{4}\)