Solve 5/2x+9=x+15/2

$$\frac { 5 } { 2 } x + 9 = x + \frac { 15 } { 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$\frac{5}{2}x+9-x=\frac{15}{2}$$

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

$$\frac{3}{2}x+9=\frac{15}{2}$$

Subtract 9 from both sides.

$$\frac{3}{2}x=\frac{15}{2}-9$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{3}{2}x=\frac{15}{2}-\frac{18}{2}$$

Since \frac{15}{2} and \frac{18}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}x=\frac{15-18}{2}$$

Subtract 18 from 15 to get -3.

$$\frac{3}{2}x=-\frac{3}{2}$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x=-\frac{3}{2}\times \frac{2}{3}$$

Multiply -\frac{3}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3\times 2}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

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

Divide -3 by 3 to get -1.

$$x=-1$$