Solve 1/2(-2+2x)=-5/4(-3-2x)

$$\frac { 1 } { 2 } ( - 2 + 2 x ) = - \frac { 5 } { 4 } ( - 3 - 2 x )$$

Solve for x

$$x = -\frac{19}{6} = -3\frac{1}{6} \approx -3.166666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by -2+2x.

$$\frac{1}{2}\left(-2\right)+\frac{1}{2}\times 2x=-\frac{5}{4}\left(-3-2x\right)$$

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

$$\frac{-2}{2}+\frac{1}{2}\times 2x=-\frac{5}{4}\left(-3-2x\right)$$

Divide -2 by 2 to get -1.

$$-1+\frac{1}{2}\times 2x=-\frac{5}{4}\left(-3-2x\right)$$

Cancel out 2 and 2.

$$-1+x=-\frac{5}{4}\left(-3-2x\right)$$

Use the distributive property to multiply -\frac{5}{4} by -3-2x.

$$-1+x=-\frac{5}{4}\left(-3\right)-\frac{5}{4}\left(-2\right)x$$

Express -\frac{5}{4}\left(-3\right) as a single fraction.

$$-1+x=\frac{-5\left(-3\right)}{4}-\frac{5}{4}\left(-2\right)x$$

Multiply -5 and -3 to get 15.

$$-1+x=\frac{15}{4}-\frac{5}{4}\left(-2\right)x$$

Express -\frac{5}{4}\left(-2\right) as a single fraction.

$$-1+x=\frac{15}{4}+\frac{-5\left(-2\right)}{4}x$$

Multiply -5 and -2 to get 10.

$$-1+x=\frac{15}{4}+\frac{10}{4}x$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$-1+x=\frac{15}{4}+\frac{5}{2}x$$

Subtract \frac{5}{2}x from both sides.

$$-1+x-\frac{5}{2}x=\frac{15}{4}$$

Combine x and -\frac{5}{2}x to get -\frac{3}{2}x.

$$-1-\frac{3}{2}x=\frac{15}{4}$$

Add 1 to both sides.

$$-\frac{3}{2}x=\frac{15}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{3}{2}x=\frac{15}{4}+\frac{4}{4}$$

Since \frac{15}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$-\frac{3}{2}x=\frac{15+4}{4}$$

Add 15 and 4 to get 19.

$$-\frac{3}{2}x=\frac{19}{4}$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$x=\frac{19}{4}\left(-\frac{2}{3}\right)$$

Multiply \frac{19}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\left(-2\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{19\left(-2\right)}{4\times 3}.

$$x=\frac{-38}{12}$$

Reduce the fraction \frac{-38}{12} to lowest terms by extracting and canceling out 2.

$$x=-\frac{19}{6}$$