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

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

Solve for x

$$x=\frac{11}{14}\approx 0.785714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by 2x-1.

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

Express \frac{3}{4}\times 2 as a single fraction.

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

Multiply 3 and 2 to get 6.

$$\frac{6}{4}x+\frac{3}{4}\left(-1\right)=2-2x$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

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

Add 2x to both sides.

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

Combine \frac{3}{2}x and 2x to get \frac{7}{2}x.

$$\frac{7}{2}x-\frac{3}{4}=2$$

Add \frac{3}{4} to both sides.

$$\frac{7}{2}x=2+\frac{3}{4}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{7}{2}x=\frac{8}{4}+\frac{3}{4}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{2}x=\frac{8+3}{4}$$

Add 8 and 3 to get 11.

$$\frac{7}{2}x=\frac{11}{4}$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$x=\frac{11}{4}\times \frac{2}{7}$$

Multiply \frac{11}{4} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\times 2}{4\times 7}$$

Do the multiplications in the fraction \frac{11\times 2}{4\times 7}.

$$x=\frac{22}{28}$$

Reduce the fraction \frac{22}{28} to lowest terms by extracting and canceling out 2.

$$x=\frac{11}{14}$$