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

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

Solve for x

$$x = -\frac{45}{14} = -3\frac{3}{14} \approx -3.214285714$$

Steps for Solving Linear Equation

Combine \frac{1}{3}x and -\frac{3}{2}x to get -\frac{7}{6}x.

$$-\frac{7}{6}x=3+\frac{3}{4}$$

Convert 3 to fraction \frac{12}{4}.

$$-\frac{7}{6}x=\frac{12}{4}+\frac{3}{4}$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$-\frac{7}{6}x=\frac{12+3}{4}$$

Add 12 and 3 to get 15.

$$-\frac{7}{6}x=\frac{15}{4}$$

Multiply both sides by -\frac{6}{7}, the reciprocal of -\frac{7}{6}.

$$x=\frac{15}{4}\left(-\frac{6}{7}\right)$$

Multiply \frac{15}{4} times -\frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{15\left(-6\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{15\left(-6\right)}{4\times 7}.

$$x=\frac{-90}{28}$$

Reduce the fraction \frac{-90}{28} to lowest terms by extracting and canceling out 2.

$$x=-\frac{45}{14}$$