Question

solve the equation.
\\(\frac{x + 3}{3} + \frac{x + 6}{2} = 4\\)

select the correct choice below and fill in any answer boxes in your choice.

\\(\bigcirc\\) a. the solution set is \\(\\{\quad\\}\\). (type an integer or a simplified fraction.)

\\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Find common denominator

The denominators are 3 and 2, so the common denominator is 6. Multiply each term by 6:
$$6\times\frac{x + 3}{3}+6\times\frac{x + 6}{2}=6\times4$$
Simplify each term:
$$2(x + 3)+3(x + 6)=24$$

Step2: Distribute and combine like terms

Distribute the 2 and 3:
$$2x+6 + 3x+18=24$$
Combine like terms:
$$5x+24=24$$

Step3: Solve for x

Subtract 24 from both sides:
$$5x=24 - 24$$
$$5x=0$$
Divide both sides by 5:
$$x = 0$$

Answer:

A. The solution set is $\{0\}$