Question

solve.
5(x + 4) = 7(x - 2)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is x = \boxed{}. (type an integer or a fraction.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left side \(5(x + 4)\) to get \(5x+20\) and the right side \(7(x - 2)\) to get \(7x-14\). So the equation becomes \(5x + 20=7x-14\).

Step2: Move like terms together

Subtract \(5x\) from both sides: \(5x+20 - 5x=7x-14 - 5x\), which simplifies to \(20 = 2x-14\). Then add 14 to both sides: \(20 + 14=2x-14 + 14\), so \(34 = 2x\).

Step3: Solve for x

Divide both sides by 2: \(\frac{34}{2}=\frac{2x}{2}\), which gives \(x = 17\).

Answer:

A. The solution is \(x=\boxed{17}\).