Question

solve the equation.
6(x + 3) = 3(2x + 4) + 6
select the correct choice below and, if necessary,
fill in the answer box to complete your choice.
a. the solution set is
(simplify your answer.)
b. the solution set is {all real numbers}
c. the solution set is ∅

Explanation:

Step1: Expand both sides

Expand the left side: \(6(x + 3)=6x + 18\)
Expand the right side: \(3(2x + 4)+6 = 6x+12 + 6=6x + 18\)

Step2: Compare both sides

We have \(6x + 18=6x + 18\). Subtract \(6x\) from both sides, we get \(18 = 18\), which is always true. So the equation is an identity and holds for all real numbers.

Answer:

B. The solution set is \{all real numbers\}