Solve 2/3x-1/2=5/4x+30

$$\frac { 2 } { 3 } x - \frac { 1 } { 2 } = \frac { 5 } { 4 } x + 30$$

Solve for x

$$x = -\frac{366}{7} = -52\frac{2}{7} \approx -52.285714286$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}x-\frac{1}{2}-\frac{5}{4}x=30$$

Combine \frac{2}{3}x and -\frac{5}{4}x to get -\frac{7}{12}x.

$$-\frac{7}{12}x-\frac{1}{2}=30$$

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

$$-\frac{7}{12}x=30+\frac{1}{2}$$

Convert 30 to fraction \frac{60}{2}.

$$-\frac{7}{12}x=\frac{60}{2}+\frac{1}{2}$$

Since \frac{60}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-\frac{7}{12}x=\frac{60+1}{2}$$

Add 60 and 1 to get 61.

$$-\frac{7}{12}x=\frac{61}{2}$$

Multiply both sides by -\frac{12}{7}, the reciprocal of -\frac{7}{12}.

$$x=\frac{61}{2}\left(-\frac{12}{7}\right)$$

Multiply \frac{61}{2} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{61\left(-12\right)}{2\times 7}$$

Do the multiplications in the fraction \frac{61\left(-12\right)}{2\times 7}.

$$x=\frac{-732}{14}$$

Reduce the fraction \frac{-732}{14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{366}{7}$$