Question

solve the equation, and check your solution.
$6 - 4x = 7x - 9x + 2$
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 $\varnothing$.

Explanation:

Step1: Combine like terms on right

$6 - 4x = (7x - 9x) + 2$
$6 - 4x = -2x + 2$

Step2: Add $4x$ to both sides

$6 - 4x + 4x = -2x + 2 + 4x$
$6 = 2x + 2$

Step3: Subtract 2 from both sides

$6 - 2 = 2x + 2 - 2$
$4 = 2x$

Step4: Divide by 2 on both sides

$\frac{4}{2} = \frac{2x}{2}$
$2 = x$

Step5: Verify the solution

Substitute $x=2$ into original equation:
Left side: $6 - 4(2) = 6 - 8 = -2$
Right side: $7(2) - 9(2) + 2 = 14 - 18 + 2 = -2$
Both sides are equal, so solution is valid.

Answer:

A. The solution set is {2}