Solve -x+1/2x=67/12+x+5/3-2

$$- x + \frac { 1 } { 2 } x = \frac { 67 } { 12 } + x + \frac { 5 } { 3 } - 2$$

Solve for x

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps for Solving Linear Equation

Least common multiple of 12 and 3 is 12. Convert \frac{67}{12} and \frac{5}{3} to fractions with denominator 12.

$$-x+\frac{1}{2}x=\frac{67}{12}+x+\frac{20}{12}-2$$

Since \frac{67}{12} and \frac{20}{12} have the same denominator, add them by adding their numerators.

$$-x+\frac{1}{2}x=\frac{67+20}{12}+x-2$$

Add 67 and 20 to get 87.

$$-x+\frac{1}{2}x=\frac{87}{12}+x-2$$

Reduce the fraction \frac{87}{12} to lowest terms by extracting and canceling out 3.

$$-x+\frac{1}{2}x=\frac{29}{4}+x-2$$

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

$$-x+\frac{1}{2}x=\frac{29}{4}+x-\frac{8}{4}$$

Since \frac{29}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-x+\frac{1}{2}x=\frac{29-8}{4}+x$$

Subtract 8 from 29 to get 21.

$$-x+\frac{1}{2}x=\frac{21}{4}+x$$

Subtract x from both sides.

$$-x+\frac{1}{2}x-x=\frac{21}{4}$$

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

$$-x-\frac{1}{2}x=\frac{21}{4}$$

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

$$-\frac{3}{2}x=\frac{21}{4}$$

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

$$x=\frac{21}{4}\left(-\frac{2}{3}\right)$$

Multiply \frac{21}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{21\left(-2\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{21\left(-2\right)}{4\times 3}.

$$x=\frac{-42}{12}$$

Reduce the fraction \frac{-42}{12} to lowest terms by extracting and canceling out 6.

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