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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and 2 to get 4.

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

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

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

Multiply 2 and 4 to get 8.

$$\frac{4}{3}x+\frac{8}{3}=4\left(4-4x\right)+4$$

Use the distributive property to multiply 4 by 4-4x.

$$\frac{4}{3}x+\frac{8}{3}=16-16x+4$$

Add 16 and 4 to get 20.

$$\frac{4}{3}x+\frac{8}{3}=20-16x$$

Add 16x to both sides.

$$\frac{4}{3}x+\frac{8}{3}+16x=20$$

Combine \frac{4}{3}x and 16x to get \frac{52}{3}x.

$$\frac{52}{3}x+\frac{8}{3}=20$$

Subtract \frac{8}{3} from both sides.

$$\frac{52}{3}x=20-\frac{8}{3}$$

Convert 20 to fraction \frac{60}{3}.

$$\frac{52}{3}x=\frac{60}{3}-\frac{8}{3}$$

Since \frac{60}{3} and \frac{8}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52}{3}x=\frac{60-8}{3}$$

Subtract 8 from 60 to get 52.

$$\frac{52}{3}x=\frac{52}{3}$$

Multiply both sides by \frac{3}{52}, the reciprocal of \frac{52}{3}.

$$x=\frac{52}{3}\times \frac{3}{52}$$

Cancel out \frac{52}{3} and its reciprocal \frac{3}{52}.

$$x=1$$