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

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

Solve for x

$$x=13$$

Steps for Solving Linear Equation

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

$$\frac{3}{5}x+\frac{3}{5}\times 2=x-4$$

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

$$\frac{3}{5}x+\frac{3\times 2}{5}=x-4$$

Multiply 3 and 2 to get 6.

$$\frac{3}{5}x+\frac{6}{5}=x-4$$

Subtract x from both sides.

$$\frac{3}{5}x+\frac{6}{5}-x=-4$$

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

$$-\frac{2}{5}x+\frac{6}{5}=-4$$

Subtract \frac{6}{5} from both sides.

$$-\frac{2}{5}x=-4-\frac{6}{5}$$

Convert -4 to fraction -\frac{20}{5}.

$$-\frac{2}{5}x=-\frac{20}{5}-\frac{6}{5}$$

Since -\frac{20}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{5}x=\frac{-20-6}{5}$$

Subtract 6 from -20 to get -26.

$$-\frac{2}{5}x=-\frac{26}{5}$$

Multiply both sides by -\frac{5}{2}, the reciprocal of -\frac{2}{5}.

$$x=-\frac{26}{5}\left(-\frac{5}{2}\right)$$

Multiply -\frac{26}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-26\left(-5\right)}{5\times 2}$$

Do the multiplications in the fraction \frac{-26\left(-5\right)}{5\times 2}.

$$x=\frac{130}{10}$$

Divide 130 by 10 to get 13.

$$x=13$$