Solve 5x/4-x/7=2x-3/14+x/2

$$\frac { 5 x } { 4 } - \frac { x } { 7 } = \frac { 2 x - 3 } { 14 } + \frac { x } { 2 }$$

Solve for x

$$x=-\frac{6}{13}\approx -0.461538462$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 4,7,14,2.

$$7\times 5x-4x=2\left(2x-3\right)+14x$$

Multiply 7 and 5 to get 35.

$$35x-4x=2\left(2x-3\right)+14x$$

Combine 35x and -4x to get 31x.

$$31x=2\left(2x-3\right)+14x$$

Use the distributive property to multiply 2 by 2x-3.

$$31x=4x-6+14x$$

Combine 4x and 14x to get 18x.

$$31x=18x-6$$

Subtract 18x from both sides.

$$31x-18x=-6$$

Combine 31x and -18x to get 13x.

$$13x=-6$$

Divide both sides by 13.

$$x=\frac{-6}{13}$$

Fraction \frac{-6}{13} can be rewritten as -\frac{6}{13} by extracting the negative sign.

$$x=-\frac{6}{13}$$