Solve the equation.
$\frac{2x+4}{x-1}=5$

• A. $x=3$
• B. $x=1$
• C. $x=5$
• D. No solution

Answer: (A)

Verified step by step guidance

1. Start with the given equation: \(\frac{2x+4}{x-1} = 5\).
2. To eliminate the fraction, multiply both sides of the equation by the denominator \((x-1)\) to get rid of the fraction: \((x-1) \times \frac{2x+4}{x-1} = 5 \times (x-1)\).
3. Simplify both sides: the left side becomes \(2x + 4\), and the right side becomes \(5(x - 1)\), so the equation is now \(2x + 4 = 5(x - 1)\).
4. Distribute the 5 on the right side: \(2x + 4 = 5x - 5\).
5. Next, get all terms involving \(x\) on one side and constants on the other side by subtracting \$2x\( from both sides and adding 5 to both sides: \(4 + 5 = 5x - 2x\), which simplifies to \(9 = 3x\). Then solve for \)x$ by dividing both sides by 3.