Solve 1/5x+1/2=5/2x+1

$$\frac { 1 } { 5 } x + \frac { 1 } { 2 } = \frac { 5 } { 2 } x + 1$$

Solve for x

$$x=-\frac{5}{23}\approx -0.217391304$$

Steps for Solving Linear Equation

Subtract \frac{5}{2}x from both sides.

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

Combine \frac{1}{5}x and -\frac{5}{2}x to get -\frac{23}{10}x.

$$-\frac{23}{10}x+\frac{1}{2}=1$$

Subtract \frac{1}{2} from both sides.

$$-\frac{23}{10}x=1-\frac{1}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{23}{10}x=\frac{2}{2}-\frac{1}{2}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{23}{10}x=\frac{2-1}{2}$$

Subtract 1 from 2 to get 1.

$$-\frac{23}{10}x=\frac{1}{2}$$

Multiply both sides by -\frac{10}{23}, the reciprocal of -\frac{23}{10}.

$$x=\frac{1}{2}\left(-\frac{10}{23}\right)$$

Multiply \frac{1}{2} times -\frac{10}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-10\right)}{2\times 23}$$

Do the multiplications in the fraction \frac{1\left(-10\right)}{2\times 23}.

$$x=\frac{-10}{46}$$

Reduce the fraction \frac{-10}{46} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{23}$$