Solve (2+x)/3-a=11

$$\frac { ( 2 + x ) } { 3 - a } = 11$$

Solve for a

$$a=\frac{31-x}{11}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Variable a cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by -a+3.

$$2+x=11\left(-a+3\right)$$

Use the distributive property to multiply 11 by -a+3.

$$2+x=-11a+33$$

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

$$-11a+33=2+x$$

Subtract 33 from both sides.

$$-11a=2+x-33$$

Subtract 33 from 2 to get -31.

$$-11a=-31+x$$

The equation is in standard form.

$$-11a=x-31$$

Divide both sides by -11.

$$\frac{-11a}{-11}=\frac{x-31}{-11}$$

Dividing by -11 undoes the multiplication by -11.

$$a=\frac{x-31}{-11}$$

Divide -31+x by -11.

$$a=\frac{31-x}{11}$$

Variable a cannot be equal to 3.

$$a=\frac{31-x}{11}\text{, }a\neq 3$$

Solve for x

$$x=31-11a$$

$$a\neq 3$$

Solution Steps

Multiply both sides of the equation by -a+3.

$$2+x=11\left(-a+3\right)$$

Use the distributive property to multiply 11 by -a+3.

$$2+x=-11a+33$$

Subtract 2 from both sides.

$$x=-11a+33-2$$

Subtract 2 from 33 to get 31.

$$x=-11a+31$$