Question

what is the value of x in the equation $2.5(6x - 4)=10 + 4(1.5 + 0.5x)$?
$\frac{1}{3}$
$\frac{1}{2}$
2
13

Explanation:

Step1: Expand both sides

First, expand the left - hand side: \(2.5(6x - 4)=2.5\times6x-2.5\times4 = 15x-10\)
Then, expand the right - hand side: \(10 + 4(1.5+0.5x)=10+4\times1.5 + 4\times0.5x=10 + 6+2x=16 + 2x\)
So the equation becomes \(15x-10=16 + 2x\)

Step2: Move terms with x to one side

Subtract \(2x\) from both sides: \(15x-2x-10=16+2x - 2x\), which simplifies to \(13x-10 = 16\)

Step3: Solve for x

Add 10 to both sides: \(13x-10 + 10=16 + 10\), so \(13x=26\)
Divide both sides by 13: \(x=\frac{26}{13}=2\)

Answer:

2 (corresponding to the option "2")