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

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

Solve for x

$$x=\frac{1}{32}=0.03125$$

Steps for Solving Linear Equation

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

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

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

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

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

Express \frac{2}{7}\times 3 as a single fraction.

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

Multiply 2 and 3 to get 6.

$$\frac{1}{3}-\frac{2}{3}x=\frac{6}{7}x+\frac{2}{7}$$

Subtract \frac{6}{7}x from both sides.

$$\frac{1}{3}-\frac{2}{3}x-\frac{6}{7}x=\frac{2}{7}$$

Combine -\frac{2}{3}x and -\frac{6}{7}x to get -\frac{32}{21}x.

$$\frac{1}{3}-\frac{32}{21}x=\frac{2}{7}$$

Subtract \frac{1}{3} from both sides.

$$-\frac{32}{21}x=\frac{2}{7}-\frac{1}{3}$$

Least common multiple of 7 and 3 is 21. Convert \frac{2}{7} and \frac{1}{3} to fractions with denominator 21.

$$-\frac{32}{21}x=\frac{6}{21}-\frac{7}{21}$$

Since \frac{6}{21} and \frac{7}{21} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{32}{21}x=\frac{6-7}{21}$$

Subtract 7 from 6 to get -1.

$$-\frac{32}{21}x=-\frac{1}{21}$$

Multiply both sides by -\frac{21}{32}, the reciprocal of -\frac{32}{21}.

$$x=-\frac{1}{21}\left(-\frac{21}{32}\right)$$

Multiply -\frac{1}{21} times -\frac{21}{32} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-\left(-21\right)}{21\times 32}$$

Do the multiplications in the fraction \frac{-\left(-21\right)}{21\times 32}.

$$x=\frac{21}{672}$$

Reduce the fraction \frac{21}{672} to lowest terms by extracting and canceling out 21.

$$x=\frac{1}{32}$$