Question

solve the following equation. check your solution.
6(x + 5) = 2(3x + 5) + 20

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

Explanation:

Step1: Expand both sides

Expand the left side: \(6(x + 5)=6x + 30\)
Expand the right side: \(2(3x + 5)+20 = 6x+10 + 20=6x + 30\)

Step2: Analyze the equation

After expanding, we get \(6x + 30=6x + 30\)
Subtract \(6x\) from both sides: \(30 = 30\)
This is a true statement for all real values of \(x\).

Answer:

B. The solution is all real numbers.