Question

solve the equation for x
5(x + 3) - 2 = 2x + 3(5 + x)

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

Explanation:

Step1: Expand both sides

Left side: $5(x + 3)-2 = 5x+15 - 2=5x + 13$
Right side: $2x+3(5 + x)=2x + 15+3x=5x + 15$

Step2: Subtract \(5x\) from both sides

Left: \(5x + 13-5x=13\)
Right: \(5x + 15-5x = 15\)

Step3: Analyze the result

We get \(13 = 15\), which is a false statement. So the equation has no solution.

Answer:

C. There is no solution