Solve x+x+1/2=x3-x+2/3=

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

Solve for x

$$x=\frac{6x_{3}-7}{11}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

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

Use the distributive property to multiply 3 by x+1.

$$6x+3x+3=6x_{3}-2\left(x+2\right)$$

Combine 6x and 3x to get 9x.

$$9x+3=6x_{3}-2\left(x+2\right)$$

Use the distributive property to multiply -2 by x+2.

$$9x+3=6x_{3}-2x-4$$

Add 2x to both sides.

$$9x+3+2x=6x_{3}-4$$

Combine 9x and 2x to get 11x.

$$11x+3=6x_{3}-4$$

Subtract 3 from both sides.

$$11x=6x_{3}-4-3$$

Subtract 3 from -4 to get -7.

$$11x=6x_{3}-7$$

Divide both sides by 11.

$$\frac{11x}{11}=\frac{6x_{3}-7}{11}$$

Dividing by 11 undoes the multiplication by 11.

$$x=\frac{6x_{3}-7}{11}$$

Solve for x_3

$$x_{3}=\frac{11x+7}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

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

Use the distributive property to multiply 3 by x+1.

$$6x+3x+3=6x_{3}-2\left(x+2\right)$$

Combine 6x and 3x to get 9x.

$$9x+3=6x_{3}-2\left(x+2\right)$$

Use the distributive property to multiply -2 by x+2.

$$9x+3=6x_{3}-2x-4$$

Swap sides so that all variable terms are on the left hand side.

$$6x_{3}-2x-4=9x+3$$

Add 2x to both sides.

$$6x_{3}-4=9x+3+2x$$

Combine 9x and 2x to get 11x.

$$6x_{3}-4=11x+3$$

Add 4 to both sides.

$$6x_{3}=11x+3+4$$

Add 3 and 4 to get 7.

$$6x_{3}=11x+7$$

Divide both sides by 6.

$$\frac{6x_{3}}{6}=\frac{11x+7}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x_{3}=\frac{11x+7}{6}$$