Solve 2/5(3x+7)=4(3-3x)+4

$$\frac { 2 } { 5 } ( 3 x + 7 ) = 4 ( 3 - 3 x ) + 4$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by 3x+7.

$$\frac{2}{5}\times 3x+\frac{2}{5}\times 7=4\left(3-3x\right)+4$$

Express \frac{2}{5}\times 3 as a single fraction.

$$\frac{2\times 3}{5}x+\frac{2}{5}\times 7=4\left(3-3x\right)+4$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5}x+\frac{2}{5}\times 7=4\left(3-3x\right)+4$$

Express \frac{2}{5}\times 7 as a single fraction.

$$\frac{6}{5}x+\frac{2\times 7}{5}=4\left(3-3x\right)+4$$

Multiply 2 and 7 to get 14.

$$\frac{6}{5}x+\frac{14}{5}=4\left(3-3x\right)+4$$

Use the distributive property to multiply 4 by 3-3x.

$$\frac{6}{5}x+\frac{14}{5}=12-12x+4$$

Add 12 and 4 to get 16.

$$\frac{6}{5}x+\frac{14}{5}=16-12x$$

Add 12x to both sides.

$$\frac{6}{5}x+\frac{14}{5}+12x=16$$

Combine \frac{6}{5}x and 12x to get \frac{66}{5}x.

$$\frac{66}{5}x+\frac{14}{5}=16$$

Subtract \frac{14}{5} from both sides.

$$\frac{66}{5}x=16-\frac{14}{5}$$

Convert 16 to fraction \frac{80}{5}.

$$\frac{66}{5}x=\frac{80}{5}-\frac{14}{5}$$

Since \frac{80}{5} and \frac{14}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{66}{5}x=\frac{80-14}{5}$$

Subtract 14 from 80 to get 66.

$$\frac{66}{5}x=\frac{66}{5}$$

Multiply both sides by \frac{5}{66}, the reciprocal of \frac{66}{5}.

$$x=\frac{66}{5}\times \frac{5}{66}$$

Cancel out \frac{66}{5} and its reciprocal \frac{5}{66}.

$$x=1$$