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

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

Solve for x

$$x = -\frac{27}{20} = -1\frac{7}{20} = -1.35$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{9}{7} by x+1.

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

Combine \frac{2}{3}x and \frac{9}{7}x to get \frac{41}{21}x.

$$\frac{41}{21}x+\frac{9}{7}=x$$

Subtract x from both sides.

$$\frac{41}{21}x+\frac{9}{7}-x=0$$

Combine \frac{41}{21}x and -x to get \frac{20}{21}x.

$$\frac{20}{21}x+\frac{9}{7}=0$$

Subtract \frac{9}{7} from both sides. Anything subtracted from zero gives its negation.

$$\frac{20}{21}x=-\frac{9}{7}$$

Multiply both sides by \frac{21}{20}, the reciprocal of \frac{20}{21}.

$$x=-\frac{9}{7}\times \frac{21}{20}$$

Multiply -\frac{9}{7} times \frac{21}{20} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\times 21}{7\times 20}$$

Do the multiplications in the fraction \frac{-9\times 21}{7\times 20}.

$$x=\frac{-189}{140}$$

Reduce the fraction \frac{-189}{140} to lowest terms by extracting and canceling out 7.

$$x=-\frac{27}{20}$$