Question

solve and check the following linear equation. 5x-(3x - 3)=9 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is { }. (type an integer or a simplified fraction.) b. the solution set is {x|x is all real number}. c. the solution set is ∅.

Explanation:

Step1: Remove parentheses

$5x - 3x+3 = 9$

Step2: Combine like - terms

$(5x - 3x)+3 = 9$, so $2x+3 = 9$

Step3: Isolate the variable term

Subtract 3 from both sides: $2x+3 - 3=9 - 3$, which gives $2x = 6$

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{6}{2}$, so $x = 3$

Step5: Check the solution

Substitute $x = 3$ into the original equation: $5\times3-(3\times3 - 3)=15-(9 - 3)=15 - 6=9$

Answer:

A. The solution set is $\{3\}$