Solve 2x-4=-1/2x+7/2

$$2 x - 4 = - \frac { 1 } { 2 } x + \frac { 7 } { 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Add \frac{1}{2}x to both sides.

$$2x-4+\frac{1}{2}x=\frac{7}{2}$$

Combine 2x and \frac{1}{2}x to get \frac{5}{2}x.

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

Add 4 to both sides.

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

Convert 4 to fraction \frac{8}{2}.

$$\frac{5}{2}x=\frac{7}{2}+\frac{8}{2}$$

Since \frac{7}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{5}{2}x=\frac{7+8}{2}$$

Add 7 and 8 to get 15.

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

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$x=\frac{15}{2}\times \frac{2}{5}$$

Multiply \frac{15}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{15\times 2}{2\times 5}$$

Cancel out 2 in both numerator and denominator.

$$x=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x=3$$