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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by x-1.

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

Multiply \frac{2}{5} and -1 to get -\frac{2}{5}.

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

Use the distributive property to multiply \frac{8}{5} by x+2.

$$\frac{2}{5}x-\frac{2}{5}+\frac{8}{5}x+\frac{8}{5}\times 2=3x-\frac{1}{5}$$

Express \frac{8}{5}\times 2 as a single fraction.

$$\frac{2}{5}x-\frac{2}{5}+\frac{8}{5}x+\frac{8\times 2}{5}=3x-\frac{1}{5}$$

Multiply 8 and 2 to get 16.

$$\frac{2}{5}x-\frac{2}{5}+\frac{8}{5}x+\frac{16}{5}=3x-\frac{1}{5}$$

Combine \frac{2}{5}x and \frac{8}{5}x to get 2x.

$$2x-\frac{2}{5}+\frac{16}{5}=3x-\frac{1}{5}$$

Since -\frac{2}{5} and \frac{16}{5} have the same denominator, add them by adding their numerators.

$$2x+\frac{-2+16}{5}=3x-\frac{1}{5}$$

Add -2 and 16 to get 14.

$$2x+\frac{14}{5}=3x-\frac{1}{5}$$

Subtract 3x from both sides.

$$2x+\frac{14}{5}-3x=-\frac{1}{5}$$

Combine 2x and -3x to get -x.

$$-x+\frac{14}{5}=-\frac{1}{5}$$

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

$$-x=-\frac{1}{5}-\frac{14}{5}$$

Since -\frac{1}{5} and \frac{14}{5} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{-1-14}{5}$$

Subtract 14 from -1 to get -15.

$$-x=\frac{-15}{5}$$

Divide -15 by 5 to get -3.

$$-x=-3$$

Multiply both sides by -1.

$$x=3$$