Solve 3(2/3*1/6)-3/4(2x+18)=-4

$$3 ( \frac { 2 } { 3 } \times \frac { 1 } { 6 } ) - \frac { 3 } { 4 } ( 2 x + 18 ) = - 4$$

Solve for x

$$x = -\frac{55}{9} = -6\frac{1}{9} \approx -6.111111111$$

Steps for Solving Linear Equation

Cancel out 3 and 3.

$$2\times \frac{1}{6}-\frac{3}{4}\left(2x+18\right)=-4$$

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$\frac{2}{6}-\frac{3}{4}\left(2x+18\right)=-4$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}-\frac{3}{4}\left(2x+18\right)=-4$$

Use the distributive property to multiply -\frac{3}{4} by 2x+18.

$$\frac{1}{3}-\frac{3}{4}\times 2x-\frac{3}{4}\times 18=-4$$

Express -\frac{3}{4}\times 2 as a single fraction.

$$\frac{1}{3}+\frac{-3\times 2}{4}x-\frac{3}{4}\times 18=-4$$

Multiply -3 and 2 to get -6.

$$\frac{1}{3}+\frac{-6}{4}x-\frac{3}{4}\times 18=-4$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}-\frac{3}{2}x-\frac{3}{4}\times 18=-4$$

Express -\frac{3}{4}\times 18 as a single fraction.

$$\frac{1}{3}-\frac{3}{2}x+\frac{-3\times 18}{4}=-4$$

Multiply -3 and 18 to get -54.

$$\frac{1}{3}-\frac{3}{2}x+\frac{-54}{4}=-4$$

Reduce the fraction \frac{-54}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}-\frac{3}{2}x-\frac{27}{2}=-4$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{27}{2} to fractions with denominator 6.

$$\frac{2}{6}-\frac{3}{2}x-\frac{81}{6}=-4$$

Since \frac{2}{6} and \frac{81}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-81}{6}-\frac{3}{2}x=-4$$

Subtract 81 from 2 to get -79.

$$-\frac{79}{6}-\frac{3}{2}x=-4$$

Add \frac{79}{6} to both sides.

$$-\frac{3}{2}x=-4+\frac{79}{6}$$

Convert -4 to fraction -\frac{24}{6}.

$$-\frac{3}{2}x=-\frac{24}{6}+\frac{79}{6}$$

Since -\frac{24}{6} and \frac{79}{6} have the same denominator, add them by adding their numerators.

$$-\frac{3}{2}x=\frac{-24+79}{6}$$

Add -24 and 79 to get 55.

$$-\frac{3}{2}x=\frac{55}{6}$$

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

$$x=\frac{55}{6}\left(-\frac{2}{3}\right)$$

Multiply \frac{55}{6} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{55\left(-2\right)}{6\times 3}$$

Do the multiplications in the fraction \frac{55\left(-2\right)}{6\times 3}.

$$x=\frac{-110}{18}$$

Reduce the fraction \frac{-110}{18} to lowest terms by extracting and canceling out 2.

$$x=-\frac{55}{9}$$