Solve 3/5(4x+6)=2(1-2x)+8

$$\frac { 3 } { 5 } ( 4 x + 6 ) = 2 ( 1 - 2 x ) + 8$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{5} by 4x+6.

$$\frac{3}{5}\times 4x+\frac{3}{5}\times 6=2\left(1-2x\right)+8$$

Express \frac{3}{5}\times 4 as a single fraction.

$$\frac{3\times 4}{5}x+\frac{3}{5}\times 6=2\left(1-2x\right)+8$$

Multiply 3 and 4 to get 12.

$$\frac{12}{5}x+\frac{3}{5}\times 6=2\left(1-2x\right)+8$$

Express \frac{3}{5}\times 6 as a single fraction.

$$\frac{12}{5}x+\frac{3\times 6}{5}=2\left(1-2x\right)+8$$

Multiply 3 and 6 to get 18.

$$\frac{12}{5}x+\frac{18}{5}=2\left(1-2x\right)+8$$

Use the distributive property to multiply 2 by 1-2x.

$$\frac{12}{5}x+\frac{18}{5}=2-4x+8$$

Add 2 and 8 to get 10.

$$\frac{12}{5}x+\frac{18}{5}=10-4x$$

Add 4x to both sides.

$$\frac{12}{5}x+\frac{18}{5}+4x=10$$

Combine \frac{12}{5}x and 4x to get \frac{32}{5}x.

$$\frac{32}{5}x+\frac{18}{5}=10$$

Subtract \frac{18}{5} from both sides.

$$\frac{32}{5}x=10-\frac{18}{5}$$

Convert 10 to fraction \frac{50}{5}.

$$\frac{32}{5}x=\frac{50}{5}-\frac{18}{5}$$

Since \frac{50}{5} and \frac{18}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32}{5}x=\frac{50-18}{5}$$

Subtract 18 from 50 to get 32.

$$\frac{32}{5}x=\frac{32}{5}$$

Multiply both sides by \frac{5}{32}, the reciprocal of \frac{32}{5}.

$$x=\frac{32}{5}\times \frac{5}{32}$$

Cancel out \frac{32}{5} and its reciprocal \frac{5}{32}.

$$x=1$$