Question

what is the solution to this equation? round your answer to the nearest hundredth. -0.5(x + 2) = 2(5 - x) - 3x a. x = -0.89 b. x = 1.67 c. x = -2.27 d. x = 2.44

Explanation:

Step1: Expand both sides

First, expand the left - hand side: \(-0.5(x + 2)=-0.5x-1\)
Then, expand the right - hand side: \(2(5 - x)-3x = 10-2x-3x=10 - 5x\)
So the equation becomes \(-0.5x-1 = 10-5x\)

Step2: Move terms with x to one side

Add \(5x\) to both sides of the equation: \(-0.5x + 5x-1=10-5x + 5x\)
\(4.5x-1 = 10\)

Step3: Solve for x

Add 1 to both sides: \(4.5x-1 + 1=10 + 1\)
\(4.5x=11\)
Divide both sides by \(4.5\): \(x=\frac{11}{4.5}\approx2.44\)

Answer:

D. \(x = 2.44\)