Solve 1/2x+6-x=11/4

$$\frac{ 1 }{ 2 } x+6-x = \frac{ 11 }{ 4 }$$

Solve for x

$$x = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

Steps for Solving Linear Equation

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

$$-\frac{1}{2}x+6=\frac{11}{4}$$

Subtract 6 from both sides.

$$-\frac{1}{2}x=\frac{11}{4}-6$$

Convert 6 to fraction \frac{24}{4}.

$$-\frac{1}{2}x=\frac{11}{4}-\frac{24}{4}$$

Since \frac{11}{4} and \frac{24}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}x=\frac{11-24}{4}$$

Subtract 24 from 11 to get -13.

$$-\frac{1}{2}x=-\frac{13}{4}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=-\frac{13}{4}\left(-2\right)$$

Express -\frac{13}{4}\left(-2\right) as a single fraction.

$$x=\frac{-13\left(-2\right)}{4}$$

Multiply -13 and -2 to get 26.

$$x=\frac{26}{4}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{13}{2}$$