Question

solve and check the linear equation.
$4(x - 6) = 6(x + 8)$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is { }.

b. the solution set is {x | x is a real number}.

c. the solution set is $\varnothing$.

Explanation:

Step1: Expand both sides

$4x - 24 = 6x + 48$

Step2: Isolate x terms

$4x - 6x = 48 + 24$

Step3: Simplify both sides

$-2x = 72$

Step4: Solve for x

$x = \frac{72}{-2} = -36$

Step5: Verify the solution

Substitute $x=-36$ into original equation:
Left side: $4(-36 - 6) = 4(-42) = -168$
Right side: $6(-36 + 8) = 6(-28) = -168$
Both sides are equal, so $x=-36$ is valid.

Answer:

A. The solution set is $\{-36\}$.