Solve 4x+3/2-8x-6/5=x

$$\frac { 4 x + 3 } { 2 } - \frac { 8 x - 6 } { 5 } = x$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 5 is 10. Multiply \frac{4x+3}{2} times \frac{5}{5}. Multiply \frac{8x-6}{5} times \frac{2}{2}.

$$\frac{5\left(4x+3\right)}{10}-\frac{2\left(8x-6\right)}{10}=x$$

Since \frac{5\left(4x+3\right)}{10} and \frac{2\left(8x-6\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(4x+3\right)-2\left(8x-6\right)}{10}=x$$

Do the multiplications in 5\left(4x+3\right)-2\left(8x-6\right).

$$\frac{20x+15-16x+12}{10}=x$$

Combine like terms in 20x+15-16x+12.

$$\frac{4x+27}{10}=x$$

Divide each term of 4x+27 by 10 to get \frac{2}{5}x+\frac{27}{10}.

$$\frac{2}{5}x+\frac{27}{10}=x$$

Subtract x from both sides.

$$\frac{2}{5}x+\frac{27}{10}-x=0$$

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

$$-\frac{3}{5}x+\frac{27}{10}=0$$

Subtract \frac{27}{10} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{3}{5}x=-\frac{27}{10}$$

Multiply both sides by -\frac{5}{3}, the reciprocal of -\frac{3}{5}.

$$x=-\frac{27}{10}\left(-\frac{5}{3}\right)$$

Multiply -\frac{27}{10} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-27\left(-5\right)}{10\times 3}$$

Do the multiplications in the fraction \frac{-27\left(-5\right)}{10\times 3}.

$$x=\frac{135}{30}$$

Reduce the fraction \frac{135}{30} to lowest terms by extracting and canceling out 15.

$$x=\frac{9}{2}$$