Question

1. 6r - 33 = 7(3r + 6)

Explanation:

Step1: Expand the right side

Using the distributive property \(a(b + c)=ab+ac\), we get \(7(3r + 6)=7\times3r+7\times6 = 21r+42\). So the equation becomes \(6r - 33=21r + 42\).

Step2: Move variable terms to one side

Subtract \(6r\) from both sides: \(6r-6r - 33=21r-6r + 42\), which simplifies to \(-33 = 15r+42\).

Step3: Move constant terms to the other side

Subtract \(42\) from both sides: \(-33 - 42=15r+42 - 42\), so \(-75 = 15r\).

Step4: Solve for r

Divide both sides by \(15\): \(\frac{-75}{15}=\frac{15r}{15}\), which gives \(r=- 5\).

Answer:

\(r = - 5\)