Solve x+x+1=2/3x+9/2(x+1)

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

Solve for x

$$x = -\frac{21}{19} = -1\frac{2}{19} \approx -1.105263158$$

Steps for Solving Linear Equation

Combine x and x to get 2x.

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

Use the distributive property to multiply \frac{9}{2} by x+1.

$$2x+1=\frac{2}{3}x+\frac{9}{2}x+\frac{9}{2}$$

Combine \frac{2}{3}x and \frac{9}{2}x to get \frac{31}{6}x.

$$2x+1=\frac{31}{6}x+\frac{9}{2}$$

Subtract \frac{31}{6}x from both sides.

$$2x+1-\frac{31}{6}x=\frac{9}{2}$$

Combine 2x and -\frac{31}{6}x to get -\frac{19}{6}x.

$$-\frac{19}{6}x+1=\frac{9}{2}$$

Subtract 1 from both sides.

$$-\frac{19}{6}x=\frac{9}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{19}{6}x=\frac{9}{2}-\frac{2}{2}$$

Since \frac{9}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{6}x=\frac{9-2}{2}$$

Subtract 2 from 9 to get 7.

$$-\frac{19}{6}x=\frac{7}{2}$$

Multiply both sides by -\frac{6}{19}, the reciprocal of -\frac{19}{6}.

$$x=\frac{7}{2}\left(-\frac{6}{19}\right)$$

Multiply \frac{7}{2} times -\frac{6}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\left(-6\right)}{2\times 19}$$

Do the multiplications in the fraction \frac{7\left(-6\right)}{2\times 19}.

$$x=\frac{-42}{38}$$

Reduce the fraction \frac{-42}{38} to lowest terms by extracting and canceling out 2.

$$x=-\frac{21}{19}$$