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

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

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Subtract \frac{3}{2}x from both sides.

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

Combine 5x and -\frac{3}{2}x to get \frac{7}{2}x.

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

Subtract \frac{7}{2} from both sides.

$$\frac{7}{2}x=-14-\frac{7}{2}$$

Convert -14 to fraction -\frac{28}{2}.

$$\frac{7}{2}x=-\frac{28}{2}-\frac{7}{2}$$

Since -\frac{28}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}x=\frac{-28-7}{2}$$

Subtract 7 from -28 to get -35.

$$\frac{7}{2}x=-\frac{35}{2}$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$x=-\frac{35}{2}\times \frac{2}{7}$$

Multiply -\frac{35}{2} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-35\times 2}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$x=\frac{-35}{7}$$

Divide -35 by 7 to get -5.

$$x=-5$$