# How do you solve 3.5x-1=-1/2(-7x+2)?

Jul 17, 2015

There are an infinite number of solutions.

#### Explanation:

Convert $3.5$ into an improper fraction.

$3.5 = 3 \frac{1}{2} = \frac{7}{2}$

Rewrite the equation.

$\frac{7}{2} x - 1 = - \frac{1}{2} \left(- 7 x + 2\right)$

Apply the distributive property on the right side.

$\frac{7}{2} x - 1 = \left(\left(- \frac{1}{2} \cdot - 7 x\right) + \left(- \frac{1}{2} \cdot 2\right)\right)$ =

$\frac{7}{2} x - 1 = \frac{7}{2} x - 1$

Because both sides are equal, there are an infinite number of solutions.