Question

what is the solution to the equation
-5(x - 1) = 2x - 3
a x = -\frac{2}{7}
b x = \frac{2}{3}
c x = 2
d x = \frac{8}{7}

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we expand \(-5(x - 1)\) to get \(-5x+5\). So the equation becomes \(-5x + 5=2x-3\).

Step2: Move all x terms to one side

Add \(5x\) to both sides of the equation: \(-5x+5 + 5x=2x-3+5x\), which simplifies to \(5 = 7x-3\).

Step3: Solve for x

Add 3 to both sides: \(5 + 3=7x-3+3\), so \(8 = 7x\). Then divide both sides by 7: \(x=\frac{8}{7}\).

Answer:

D. \(x = \frac{8}{7}\)