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

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

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

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

Express \frac{2}{3}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

$$\frac{2}{3}x+\frac{-6}{3}-\frac{1}{7}\left(x+1\right)=1$$

Divide -6 by 3 to get -2.

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

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

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

Combine \frac{2}{3}x and -\frac{1}{7}x to get \frac{11}{21}x.

$$\frac{11}{21}x-2-\frac{1}{7}=1$$

Convert -2 to fraction -\frac{14}{7}.

$$\frac{11}{21}x-\frac{14}{7}-\frac{1}{7}=1$$

Since -\frac{14}{7} and \frac{1}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{21}x+\frac{-14-1}{7}=1$$

Subtract 1 from -14 to get -15.

$$\frac{11}{21}x-\frac{15}{7}=1$$

Add \frac{15}{7} to both sides.

$$\frac{11}{21}x=1+\frac{15}{7}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{11}{21}x=\frac{7}{7}+\frac{15}{7}$$

Since \frac{7}{7} and \frac{15}{7} have the same denominator, add them by adding their numerators.

$$\frac{11}{21}x=\frac{7+15}{7}$$

Add 7 and 15 to get 22.

$$\frac{11}{21}x=\frac{22}{7}$$

Multiply both sides by \frac{21}{11}, the reciprocal of \frac{11}{21}.

$$x=\frac{22}{7}\times \frac{21}{11}$$

Multiply \frac{22}{7} times \frac{21}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{22\times 21}{7\times 11}$$

Do the multiplications in the fraction \frac{22\times 21}{7\times 11}.

$$x=\frac{462}{77}$$

Divide 462 by 77 to get 6.

$$x=6$$