Question

solve the equation, and check your solution. 6 - 2x = 5x - 9x + 20 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 ∅.

Explanation:

Step1: Simplify the right side

Combine like terms on the right: \(5x - 9x+20=-4x + 20\)
So the equation becomes \(6 - 2x=-4x + 20\)

Step2: Add \(4x\) to both sides

\(6 - 2x+4x=-4x + 20+4x\)
Simplify: \(6 + 2x=20\)

Step3: Subtract 6 from both sides

\(6 + 2x-6=20 - 6\)
Simplify: \(2x=14\)

Step4: Divide by 2

\(\frac{2x}{2}=\frac{14}{2}\)
Simplify: \(x = 7\)

Answer:

A. The solution set is \(\{7\}\)