Solve 1/7(3x+2)-1/5(x+4)=2

$$\frac { 1 } { 7 } ( 3 x + 2 ) - \frac { 1 } { 5 } ( x + 4 ) = 2$$

Solve for x

$$x=11$$

Steps for Solving Linear Equation

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

$$\frac{1}{7}\times 3x+\frac{1}{7}\times 2-\frac{1}{5}\left(x+4\right)=2$$

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

$$\frac{3}{7}x+\frac{1}{7}\times 2-\frac{1}{5}\left(x+4\right)=2$$

Multiply \frac{1}{7} and 2 to get \frac{2}{7}.

$$\frac{3}{7}x+\frac{2}{7}-\frac{1}{5}\left(x+4\right)=2$$

Use the distributive property to multiply -\frac{1}{5} by x+4.

$$\frac{3}{7}x+\frac{2}{7}-\frac{1}{5}x-\frac{1}{5}\times 4=2$$

Express -\frac{1}{5}\times 4 as a single fraction.

$$\frac{3}{7}x+\frac{2}{7}-\frac{1}{5}x+\frac{-4}{5}=2$$

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

$$\frac{3}{7}x+\frac{2}{7}-\frac{1}{5}x-\frac{4}{5}=2$$

Combine \frac{3}{7}x and -\frac{1}{5}x to get \frac{8}{35}x.

$$\frac{8}{35}x+\frac{2}{7}-\frac{4}{5}=2$$

Least common multiple of 7 and 5 is 35. Convert \frac{2}{7} and \frac{4}{5} to fractions with denominator 35.

$$\frac{8}{35}x+\frac{10}{35}-\frac{28}{35}=2$$

Since \frac{10}{35} and \frac{28}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{35}x+\frac{10-28}{35}=2$$

Subtract 28 from 10 to get -18.

$$\frac{8}{35}x-\frac{18}{35}=2$$

Add \frac{18}{35} to both sides.

$$\frac{8}{35}x=2+\frac{18}{35}$$

Convert 2 to fraction \frac{70}{35}.

$$\frac{8}{35}x=\frac{70}{35}+\frac{18}{35}$$

Since \frac{70}{35} and \frac{18}{35} have the same denominator, add them by adding their numerators.

$$\frac{8}{35}x=\frac{70+18}{35}$$

Add 70 and 18 to get 88.

$$\frac{8}{35}x=\frac{88}{35}$$

Multiply both sides by \frac{35}{8}, the reciprocal of \frac{8}{35}.

$$x=\frac{88}{35}\times \frac{35}{8}$$

Multiply \frac{88}{35} times \frac{35}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{88\times 35}{35\times 8}$$

Cancel out 35 in both numerator and denominator.

$$x=\frac{88}{8}$$

Divide 88 by 8 to get 11.

$$x=11$$