Solve 1/9(x+5)=1/8(x-7)+1

$$\frac { 1 } { 9 } ( x + 5 ) = \frac { 1 } { 8 } ( x - 7 ) + 1$$

Solve for x

$$x=31$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{9} by x+5.

$$\frac{1}{9}x+\frac{1}{9}\times 5=\frac{1}{8}\left(x-7\right)+1$$

Multiply \frac{1}{9} and 5 to get \frac{5}{9}.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}\left(x-7\right)+1$$

Use the distributive property to multiply \frac{1}{8} by x-7.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}x+\frac{1}{8}\left(-7\right)+1$$

Multiply \frac{1}{8} and -7 to get \frac{-7}{8}.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}x+\frac{-7}{8}+1$$

Fraction \frac{-7}{8} can be rewritten as -\frac{7}{8} by extracting the negative sign.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}x-\frac{7}{8}+1$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}x-\frac{7}{8}+\frac{8}{8}$$

Since -\frac{7}{8} and \frac{8}{8} have the same denominator, add them by adding their numerators.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}x+\frac{-7+8}{8}$$

Add -7 and 8 to get 1.

$$\frac{1}{9}x+\frac{5}{9}=\frac{1}{8}x+\frac{1}{8}$$

Subtract \frac{1}{8}x from both sides.

$$\frac{1}{9}x+\frac{5}{9}-\frac{1}{8}x=\frac{1}{8}$$

Combine \frac{1}{9}x and -\frac{1}{8}x to get -\frac{1}{72}x.

$$-\frac{1}{72}x+\frac{5}{9}=\frac{1}{8}$$

Subtract \frac{5}{9} from both sides.

$$-\frac{1}{72}x=\frac{1}{8}-\frac{5}{9}$$

Least common multiple of 8 and 9 is 72. Convert \frac{1}{8} and \frac{5}{9} to fractions with denominator 72.

$$-\frac{1}{72}x=\frac{9}{72}-\frac{40}{72}$$

Since \frac{9}{72} and \frac{40}{72} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{72}x=\frac{9-40}{72}$$

Subtract 40 from 9 to get -31.

$$-\frac{1}{72}x=-\frac{31}{72}$$

Multiply both sides by -72, the reciprocal of -\frac{1}{72}.

$$x=-\frac{31}{72}\left(-72\right)$$

Express -\frac{31}{72}\left(-72\right) as a single fraction.

$$x=\frac{-31\left(-72\right)}{72}$$

Multiply -31 and -72 to get 2232.

$$x=\frac{2232}{72}$$

Divide 2232 by 72 to get 31.

$$x=31$$