Question

Solve \(\frac{1}{3}(7 x+5)=3 x-5\) A 15 B -5 C 10 D \(\frac{-5}{2}\)

Short answer

C 10

Step-by-step solution

Distribute the 1/3 to terms inside the parentheses

Multiply each term inside the parentheses on the left side of the equation by 1/3. This results in \(\frac{1}{3} * 7x + \frac{1}{3} * 5 = 3x - 5\), which simplifies to \(\frac{7}{3}x + \frac{5}{3} = 3x - 5\).

Simplify the equation

In order to isolate \(x\), you must first move the \(x\) terms to one side and the constant terms to the other side. To do so, subtract \(\frac{7}{3}x\) from both sides of the equation, which results in \(\frac{5}{3} = 3x - \frac{7}{3}x - 5\). Secondly, add 5 to both sides of the equation, resulting in \(\frac{5}{3} + 5 = 3x - \frac{7}{3}x\). This simplifies to \(\frac{20}{3} = \frac{2}{3}x\).

Solve for x

Finally, to solve for \(x\), divide both sides of the equation by \(\frac{2}{3}\). This gives \(x = \frac{20}{3} / \frac{2}{3}\), which simplifies to \(x = 10\).