Question

6 + 8(4q - 9) = 10q

Explanation:

Step1: Distribute the 8

We use the distributive property \(a(b - c)=ab - ac\) to expand \(8(4q - 9)\). So we get \(6+8\times4q-8\times9 = 10q\), which simplifies to \(6 + 32q-72=10q\).

Step2: Combine like terms

Combine the constant terms \(6\) and \(- 72\). \(6-72=-66\), so the equation becomes \(32q-66 = 10q\).

Step3: Subtract 10q from both sides

Subtract \(10q\) from each side to get all the \(q\) terms on one side. \(32q-10q-66=10q - 10q\), which simplifies to \(22q-66 = 0\).

Step4: Add 66 to both sides

Add \(66\) to both sides of the equation. \(22q-66 + 66=0 + 66\), so we have \(22q=66\).

Step5: Divide by 22

Divide both sides by \(22\) to solve for \(q\). \(\frac{22q}{22}=\frac{66}{22}\), which gives \(q = 3\).

Answer:

\(q = 3\)