Question

which of the following is a solution to this equation?
6r - 13 = 3r + 8
r = -2
r = 7

Explanation:

Step1: Solve the equation \(6r - 13 = 3r + 8\)

Subtract \(3r\) from both sides: \(6r - 3r - 13 = 3r - 3r + 8\), which simplifies to \(3r - 13 = 8\).

Step2: Isolate the variable term

Add 13 to both sides: \(3r - 13 + 13 = 8 + 13\), so \(3r = 21\).

Step3: Solve for \(r\)

Divide both sides by 3: \(\frac{3r}{3} = \frac{21}{3}\), giving \(r = 7\). We can also check by substituting \(r = -2\) into the original equation: Left side: \(6(-2)-13=-12 - 13=-25\), Right side: \(3(-2)+8=-6 + 8 = 2\). Since \(-25
eq2\), \(r=-2\) is not a solution. Substituting \(r = 7\): Left side: \(6(7)-13 = 42-13 = 29\), Right side: \(3(7)+8 = 21 + 8 = 29\). So \(r = 7\) is a solution.

Answer:

\(r = 7\) (or in the context of the options, the correct one is the option with \(r = 7\))