Solve -1/7(6x+13)=3/5(1/3-x)

$$- \frac { 1 } { 7 } ( 6 x + 13 ) = \frac { 3 } { 5 } ( \frac { 1 } { 3 } - x )$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{7} by 6x+13.

$$-\frac{1}{7}\times 6x-\frac{1}{7}\times 13=\frac{3}{5}\left(\frac{1}{3}-x\right)$$

Express -\frac{1}{7}\times 6 as a single fraction.

$$\frac{-6}{7}x-\frac{1}{7}\times 13=\frac{3}{5}\left(\frac{1}{3}-x\right)$$

Fraction \frac{-6}{7} can be rewritten as -\frac{6}{7} by extracting the negative sign.

$$-\frac{6}{7}x-\frac{1}{7}\times 13=\frac{3}{5}\left(\frac{1}{3}-x\right)$$

Express -\frac{1}{7}\times 13 as a single fraction.

$$-\frac{6}{7}x+\frac{-13}{7}=\frac{3}{5}\left(\frac{1}{3}-x\right)$$

Fraction \frac{-13}{7} can be rewritten as -\frac{13}{7} by extracting the negative sign.

$$-\frac{6}{7}x-\frac{13}{7}=\frac{3}{5}\left(\frac{1}{3}-x\right)$$

Use the distributive property to multiply \frac{3}{5} by \frac{1}{3}-x.

$$-\frac{6}{7}x-\frac{13}{7}=\frac{3}{5}\times \frac{1}{3}+\frac{3}{5}\left(-1\right)x$$

Multiply \frac{3}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{7}x-\frac{13}{7}=\frac{3\times 1}{5\times 3}+\frac{3}{5}\left(-1\right)x$$

Cancel out 3 in both numerator and denominator.

$$-\frac{6}{7}x-\frac{13}{7}=\frac{1}{5}+\frac{3}{5}\left(-1\right)x$$

Multiply \frac{3}{5} and -1 to get -\frac{3}{5}.

$$-\frac{6}{7}x-\frac{13}{7}=\frac{1}{5}-\frac{3}{5}x$$

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

$$-\frac{6}{7}x-\frac{13}{7}+\frac{3}{5}x=\frac{1}{5}$$

Combine -\frac{6}{7}x and \frac{3}{5}x to get -\frac{9}{35}x.

$$-\frac{9}{35}x-\frac{13}{7}=\frac{1}{5}$$

Add \frac{13}{7} to both sides.

$$-\frac{9}{35}x=\frac{1}{5}+\frac{13}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{1}{5} and \frac{13}{7} to fractions with denominator 35.

$$-\frac{9}{35}x=\frac{7}{35}+\frac{65}{35}$$

Since \frac{7}{35} and \frac{65}{35} have the same denominator, add them by adding their numerators.

$$-\frac{9}{35}x=\frac{7+65}{35}$$

Add 7 and 65 to get 72.

$$-\frac{9}{35}x=\frac{72}{35}$$

Multiply both sides by -\frac{35}{9}, the reciprocal of -\frac{9}{35}.

$$x=\frac{72}{35}\left(-\frac{35}{9}\right)$$

Multiply \frac{72}{35} times -\frac{35}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{72\left(-35\right)}{35\times 9}$$

Do the multiplications in the fraction \frac{72\left(-35\right)}{35\times 9}.

$$x=\frac{-2520}{315}$$

Divide -2520 by 315 to get -8.

$$x=-8$$