Solve 2n-3/4+2-5n=1/2n-1

$$2 n - \frac { 3 } { 4 } + 2 - 5 n = \frac { 1 } { 2 } n - 1$$

Solve for n

$$n=\frac{9}{14}\approx 0.642857143$$

Steps for Solving Linear Equation

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

$$2n-\frac{3}{4}+\frac{8}{4}-5n=\frac{1}{2}n-1$$

Since -\frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$2n+\frac{-3+8}{4}-5n=\frac{1}{2}n-1$$

Add -3 and 8 to get 5.

$$2n+\frac{5}{4}-5n=\frac{1}{2}n-1$$

Combine 2n and -5n to get -3n.

$$-3n+\frac{5}{4}=\frac{1}{2}n-1$$

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

$$-3n+\frac{5}{4}-\frac{1}{2}n=-1$$

Combine -3n and -\frac{1}{2}n to get -\frac{7}{2}n.

$$-\frac{7}{2}n+\frac{5}{4}=-1$$

Subtract \frac{5}{4} from both sides.

$$-\frac{7}{2}n=-1-\frac{5}{4}$$

Convert -1 to fraction -\frac{4}{4}.

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

Since -\frac{4}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from -4 to get -9.

$$-\frac{7}{2}n=-\frac{9}{4}$$

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

$$n=-\frac{9}{4}\left(-\frac{2}{7}\right)$$

Multiply -\frac{9}{4} times -\frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{-9\left(-2\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{-9\left(-2\right)}{4\times 7}.

$$n=\frac{18}{28}$$

Reduce the fraction \frac{18}{28} to lowest terms by extracting and canceling out 2.

$$n=\frac{9}{14}$$