Solve +3/2=6-2/3x

$$+ \frac { 3 } { 2 } = 6 - \frac { 2 } { 3 } x$$

Solve for x

$$x = \frac{27}{4} = 6\frac{3}{4} = 6.75$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$6-\frac{2}{3}x=\frac{3}{2}$$

Subtract 6 from both sides.

$$-\frac{2}{3}x=\frac{3}{2}-6$$

Convert 6 to fraction \frac{12}{2}.

$$-\frac{2}{3}x=\frac{3}{2}-\frac{12}{2}$$

Since \frac{3}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x=\frac{3-12}{2}$$

Subtract 12 from 3 to get -9.

$$-\frac{2}{3}x=-\frac{9}{2}$$

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

$$x=-\frac{9}{2}\left(-\frac{3}{2}\right)$$

Multiply -\frac{9}{2} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\left(-3\right)}{2\times 2}$$

Do the multiplications in the fraction \frac{-9\left(-3\right)}{2\times 2}.

$$x=\frac{27}{4}$$