Solve 5/9x-5/3=3/4x-1/2

$$\frac{ 5 }{ 9 } x- \frac{ 5 }{ 3 } = \frac{ 3 }{ 4 } x- \frac{ 1 }{ 2 }$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Subtract \frac{3}{4}x from both sides.

$$\frac{5}{9}x-\frac{5}{3}-\frac{3}{4}x=-\frac{1}{2}$$

Combine \frac{5}{9}x and -\frac{3}{4}x to get -\frac{7}{36}x.

$$-\frac{7}{36}x-\frac{5}{3}=-\frac{1}{2}$$

Add \frac{5}{3} to both sides.

$$-\frac{7}{36}x=-\frac{1}{2}+\frac{5}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{5}{3} to fractions with denominator 6.

$$-\frac{7}{36}x=-\frac{3}{6}+\frac{10}{6}$$

Since -\frac{3}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$-\frac{7}{36}x=\frac{-3+10}{6}$$

Add -3 and 10 to get 7.

$$-\frac{7}{36}x=\frac{7}{6}$$

Multiply both sides by -\frac{36}{7}, the reciprocal of -\frac{7}{36}.

$$x=\frac{7}{6}\left(-\frac{36}{7}\right)$$

Multiply \frac{7}{6} times -\frac{36}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\left(-36\right)}{6\times 7}$$

Cancel out 7 in both numerator and denominator.

$$x=\frac{-36}{6}$$

Divide -36 by 6 to get -6.

$$x=-6$$