Question

1. $6r - 5 = 1 + 8r - 24$

Explanation:

Step1: Simplify the right side

Combine like terms on the right side: \(1 - 24 + 8r=-23 + 8r\). So the equation becomes \(6r - 5=-23 + 8r\).

Step2: Subtract \(6r\) from both sides

Subtract \(6r\) from each side: \(6r - 5-6r=-23 + 8r-6r\), which simplifies to \(-5=-23 + 2r\).

Step3: Add 23 to both sides

Add 23 to both sides: \(-5 + 23=-23 + 2r+ 23\), so \(18 = 2r\).

Step4: Divide by 2

Divide both sides by 2: \(\frac{18}{2}=\frac{2r}{2}\), which gives \(r = 9\).

Answer:

\(r = 9\)