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

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

Solve for E

$$E=\frac{3x+1}{10}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{5} by x-3.

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

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

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

Combine -\frac{1}{5}x and \frac{1}{2}x to get \frac{3}{10}x.

$$E=\frac{3}{10}x+\frac{3}{5}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{3}{5} to get \frac{1}{10}.

$$E=\frac{3}{10}x+\frac{1}{10}$$

Solve for x

$$x=\frac{10E-1}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{5} by x-3.

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

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

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

Combine -\frac{1}{5}x and \frac{1}{2}x to get \frac{3}{10}x.

$$E=\frac{3}{10}x+\frac{3}{5}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{3}{5} to get \frac{1}{10}.

$$E=\frac{3}{10}x+\frac{1}{10}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{10}x+\frac{1}{10}=E$$

Subtract \frac{1}{10} from both sides.

$$\frac{3}{10}x=E-\frac{1}{10}$$

Divide both sides of the equation by \frac{3}{10}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{10}x}{\frac{3}{10}}=\frac{E-\frac{1}{10}}{\frac{3}{10}}$$

Dividing by \frac{3}{10} undoes the multiplication by \frac{3}{10}.

$$x=\frac{E-\frac{1}{10}}{\frac{3}{10}}$$

Divide E-\frac{1}{10} by \frac{3}{10} by multiplying E-\frac{1}{10} by the reciprocal of \frac{3}{10}.

$$x=\frac{10E-1}{3}$$