Question

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

Explanation:

Step1: Expand the left side

We use the distributive property \(a(b - c)=ab - ac\) to expand \(3(7r - 7)\). So we have \(3\times7r-3\times7 = 21r-21\). The equation becomes \(21r - 21=-6 + 6r\).

Step2: Move terms with \(r\) to one side

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

Step3: Isolate the term with \(r\)

Add 21 to both sides: \(15r-21 + 21=-6 + 21\), so \(15r = 15\).

Step4: Solve for \(r\)

Divide both sides by 15: \(\frac{15r}{15}=\frac{15}{15}\), which gives \(r = 1\).

Answer:

\(r = 1\)