Solve 2/3(x-5)+11/3(x+1)=9

$$\frac { 2 } { 3 } ( x - 5 ) + 1 \frac { 1 } { 3 } ( x + 1 ) = 9$$

Solve for x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$2\left(x-5\right)+\left(1\times 3+1\right)\left(x+1\right)=27$$

Use the distributive property to multiply 2 by x-5.

$$2x-10+\left(1\times 3+1\right)\left(x+1\right)=27$$

Multiply 1 and 3 to get 3.

$$2x-10+\left(3+1\right)\left(x+1\right)=27$$

Add 3 and 1 to get 4.

$$2x-10+4\left(x+1\right)=27$$

Use the distributive property to multiply 4 by x+1.

$$2x-10+4x+4=27$$

Combine 2x and 4x to get 6x.

$$6x-10+4=27$$

Add -10 and 4 to get -6.

$$6x-6=27$$

Add 6 to both sides.

$$6x=27+6$$

Add 27 and 6 to get 33.

$$6x=33$$

Divide both sides by 6.

$$x=\frac{33}{6}$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$x=\frac{11}{2}$$