Solve 3/10x+1/2=3/5x-1/4

$$\frac { 3 } { 10 } x + \frac { 1 } { 2 } = \frac { 3 } { 5 } x - \frac { 1 } { 4 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Subtract \frac{3}{5}x from both sides.

$$\frac{3}{10}x+\frac{1}{2}-\frac{3}{5}x=-\frac{1}{4}$$

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

$$-\frac{3}{10}x+\frac{1}{2}=-\frac{1}{4}$$

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

$$-\frac{3}{10}x=-\frac{1}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$-\frac{3}{10}x=-\frac{1}{4}-\frac{2}{4}$$

Since -\frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{10}x=\frac{-1-2}{4}$$

Subtract 2 from -1 to get -3.

$$-\frac{3}{10}x=-\frac{3}{4}$$

Multiply both sides by -\frac{10}{3}, the reciprocal of -\frac{3}{10}.

$$x=-\frac{3}{4}\left(-\frac{10}{3}\right)$$

Multiply -\frac{3}{4} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3\left(-10\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{-3\left(-10\right)}{4\times 3}.

$$x=\frac{30}{12}$$

Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

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