Solve 2a-1/2=1/2a-5

$$2 a - \frac { 1 } { 2 } = \frac { 1 } { 2 } a - 5$$

Solve for a

$$a=-3$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}a from both sides.

$$2a-\frac{1}{2}-\frac{1}{2}a=-5$$

Combine 2a and -\frac{1}{2}a to get \frac{3}{2}a.

$$\frac{3}{2}a-\frac{1}{2}=-5$$

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

$$\frac{3}{2}a=-5+\frac{1}{2}$$

Convert -5 to fraction -\frac{10}{2}.

$$\frac{3}{2}a=-\frac{10}{2}+\frac{1}{2}$$

Since -\frac{10}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}a=\frac{-10+1}{2}$$

Add -10 and 1 to get -9.

$$\frac{3}{2}a=-\frac{9}{2}$$

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

$$a=-\frac{9}{2}\times \frac{2}{3}$$

Multiply -\frac{9}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{-9\times 2}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

$$a=\frac{-9}{3}$$

Divide -9 by 3 to get -3.

$$a=-3$$