Solve 1/12x+1/9(10-x)=1

$$\frac { 1 } { 12 } x + \frac { 1 } { 9 } ( 10 - x ) = 1$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{9} by 10-x.

$$\frac{1}{12}x+\frac{1}{9}\times 10+\frac{1}{9}\left(-1\right)x=1$$

Multiply \frac{1}{9} and 10 to get \frac{10}{9}.

$$\frac{1}{12}x+\frac{10}{9}+\frac{1}{9}\left(-1\right)x=1$$

Multiply \frac{1}{9} and -1 to get -\frac{1}{9}.

$$\frac{1}{12}x+\frac{10}{9}-\frac{1}{9}x=1$$

Combine \frac{1}{12}x and -\frac{1}{9}x to get -\frac{1}{36}x.

$$-\frac{1}{36}x+\frac{10}{9}=1$$

Subtract \frac{10}{9} from both sides.

$$-\frac{1}{36}x=1-\frac{10}{9}$$

Convert 1 to fraction \frac{9}{9}.

$$-\frac{1}{36}x=\frac{9}{9}-\frac{10}{9}$$

Since \frac{9}{9} and \frac{10}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{36}x=\frac{9-10}{9}$$

Subtract 10 from 9 to get -1.

$$-\frac{1}{36}x=-\frac{1}{9}$$

Multiply both sides by -36, the reciprocal of -\frac{1}{36}.

$$x=-\frac{1}{9}\left(-36\right)$$

Express -\frac{1}{9}\left(-36\right) as a single fraction.

$$x=\frac{-\left(-36\right)}{9}$$

Multiply -1 and -36 to get 36.

$$x=\frac{36}{9}$$

Divide 36 by 9 to get 4.

$$x=4$$