Solve 1/4(x+1)=1/5(8-x)

$$\frac { 1 } { 4 } ( x + 1 ) = \frac { 1 } { 5 } ( 8 - x )$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by x+1.

$$\frac{1}{4}x+\frac{1}{4}=\frac{1}{5}\left(8-x\right)$$

Use the distributive property to multiply \frac{1}{5} by 8-x.

$$\frac{1}{4}x+\frac{1}{4}=\frac{1}{5}\times 8+\frac{1}{5}\left(-1\right)x$$

Multiply \frac{1}{5} and 8 to get \frac{8}{5}.

$$\frac{1}{4}x+\frac{1}{4}=\frac{8}{5}+\frac{1}{5}\left(-1\right)x$$

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

$$\frac{1}{4}x+\frac{1}{4}=\frac{8}{5}-\frac{1}{5}x$$

Add \frac{1}{5}x to both sides.

$$\frac{1}{4}x+\frac{1}{4}+\frac{1}{5}x=\frac{8}{5}$$

Combine \frac{1}{4}x and \frac{1}{5}x to get \frac{9}{20}x.

$$\frac{9}{20}x+\frac{1}{4}=\frac{8}{5}$$

Subtract \frac{1}{4} from both sides.

$$\frac{9}{20}x=\frac{8}{5}-\frac{1}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{8}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{9}{20}x=\frac{32}{20}-\frac{5}{20}$$

Since \frac{32}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{20}x=\frac{32-5}{20}$$

Subtract 5 from 32 to get 27.

$$\frac{9}{20}x=\frac{27}{20}$$

Multiply both sides by \frac{20}{9}, the reciprocal of \frac{9}{20}.

$$x=\frac{27}{20}\times \frac{20}{9}$$

Multiply \frac{27}{20} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{27\times 20}{20\times 9}$$

Cancel out 20 in both numerator and denominator.

$$x=\frac{27}{9}$$

Divide 27 by 9 to get 3.

$$x=3$$