Answer
The equation is an identity and the solution set is {all real numbers}
Work Step by Step
Step 1: $\frac{1}{2}(6x+20)=x+4+2(x+3)$
Step 2: $3x+10=x+4+2x+6$
Step 3: $3x+10=3x+10$
Step 4: Subtracting $3x$ from both sides, $3x-3x+10=3x-3x+10$
Step 5: Simplifying, $10=10$
Step 6: Subtracting $10$ from both sides,
$10-10=10-10$
Step 7: $0=0$
Step 8: As a result, the equation is an identity and the solution set is {all real numbers}.
