Solve 1/3(2-7x)=1/2(9+3x)

$$\frac { 1 } { 3 } ( 2 - 7 x ) = \frac { 1 } { 2 } ( 9 + 3 x )$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 2-7x.

$$\frac{1}{3}\times 2+\frac{1}{3}\left(-7\right)x=\frac{1}{2}\left(9+3x\right)$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{2}{3}+\frac{1}{3}\left(-7\right)x=\frac{1}{2}\left(9+3x\right)$$

Multiply \frac{1}{3} and -7 to get \frac{-7}{3}.

$$\frac{2}{3}+\frac{-7}{3}x=\frac{1}{2}\left(9+3x\right)$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$\frac{2}{3}-\frac{7}{3}x=\frac{1}{2}\left(9+3x\right)$$

Use the distributive property to multiply \frac{1}{2} by 9+3x.

$$\frac{2}{3}-\frac{7}{3}x=\frac{1}{2}\times 9+\frac{1}{2}\times 3x$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$\frac{2}{3}-\frac{7}{3}x=\frac{9}{2}+\frac{1}{2}\times 3x$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{2}{3}-\frac{7}{3}x=\frac{9}{2}+\frac{3}{2}x$$

Subtract \frac{3}{2}x from both sides.

$$\frac{2}{3}-\frac{7}{3}x-\frac{3}{2}x=\frac{9}{2}$$

Combine -\frac{7}{3}x and -\frac{3}{2}x to get -\frac{23}{6}x.

$$\frac{2}{3}-\frac{23}{6}x=\frac{9}{2}$$

Subtract \frac{2}{3} from both sides.

$$-\frac{23}{6}x=\frac{9}{2}-\frac{2}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{2}{3} to fractions with denominator 6.

$$-\frac{23}{6}x=\frac{27}{6}-\frac{4}{6}$$

Since \frac{27}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{23}{6}x=\frac{27-4}{6}$$

Subtract 4 from 27 to get 23.

$$-\frac{23}{6}x=\frac{23}{6}$$

Multiply both sides by -\frac{6}{23}, the reciprocal of -\frac{23}{6}.

$$x=\frac{23}{6}\left(-\frac{6}{23}\right)$$

Multiply \frac{23}{6} times -\frac{6}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{23\left(-6\right)}{6\times 23}$$

Cancel out 23 in both numerator and denominator.

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

Divide -6 by 6 to get -1.

$$x=-1$$