Solve -2x+18=1/2x+11/4

$$- 2 x + 18 = \frac { 1 } { 2 } x + \frac { 11 } { 4 }$$

Solve for x

$$x = \frac{61}{10} = 6\frac{1}{10} = 6.1$$

Steps for Solving Linear Equation

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

$$-2x+18-\frac{1}{2}x=\frac{11}{4}$$

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

$$-\frac{5}{2}x+18=\frac{11}{4}$$

Subtract 18 from both sides.

$$-\frac{5}{2}x=\frac{11}{4}-18$$

Convert 18 to fraction \frac{72}{4}.

$$-\frac{5}{2}x=\frac{11}{4}-\frac{72}{4}$$

Since \frac{11}{4} and \frac{72}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{2}x=\frac{11-72}{4}$$

Subtract 72 from 11 to get -61.

$$-\frac{5}{2}x=-\frac{61}{4}$$

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

$$x=-\frac{61}{4}\left(-\frac{2}{5}\right)$$

Multiply -\frac{61}{4} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-61\left(-2\right)}{4\times 5}$$

Do the multiplications in the fraction \frac{-61\left(-2\right)}{4\times 5}.

$$x=\frac{122}{20}$$

Reduce the fraction \frac{122}{20} to lowest terms by extracting and canceling out 2.

$$x=\frac{61}{10}$$