Solve 1/2x+1/5(x+1)+1/4(x+2)=14

$$\frac { 1 } { 2 } x + \frac { 1 } { 5 } ( x + 1 ) + \frac { 1 } { 4 } ( x + 2 ) = 14$$

Solve for x

$$x=14$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}x+\frac{1}{5}x+\frac{1}{5}+\frac{1}{4}\left(x+2\right)=14$$

Combine \frac{1}{2}x and \frac{1}{5}x to get \frac{7}{10}x.

$$\frac{7}{10}x+\frac{1}{5}+\frac{1}{4}\left(x+2\right)=14$$

Use the distributive property to multiply \frac{1}{4} by x+2.

$$\frac{7}{10}x+\frac{1}{5}+\frac{1}{4}x+\frac{1}{4}\times 2=14$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{7}{10}x+\frac{1}{5}+\frac{1}{4}x+\frac{2}{4}=14$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{10}x+\frac{1}{5}+\frac{1}{4}x+\frac{1}{2}=14$$

Combine \frac{7}{10}x and \frac{1}{4}x to get \frac{19}{20}x.

$$\frac{19}{20}x+\frac{1}{5}+\frac{1}{2}=14$$

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{19}{20}x+\frac{2}{10}+\frac{5}{10}=14$$

Since \frac{2}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{19}{20}x+\frac{2+5}{10}=14$$

Add 2 and 5 to get 7.

$$\frac{19}{20}x+\frac{7}{10}=14$$

Subtract \frac{7}{10} from both sides.

$$\frac{19}{20}x=14-\frac{7}{10}$$

Convert 14 to fraction \frac{140}{10}.

$$\frac{19}{20}x=\frac{140}{10}-\frac{7}{10}$$

Since \frac{140}{10} and \frac{7}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{20}x=\frac{140-7}{10}$$

Subtract 7 from 140 to get 133.

$$\frac{19}{20}x=\frac{133}{10}$$

Multiply both sides by \frac{20}{19}, the reciprocal of \frac{19}{20}.

$$x=\frac{133}{10}\times \frac{20}{19}$$

Multiply \frac{133}{10} times \frac{20}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{133\times 20}{10\times 19}$$

Do the multiplications in the fraction \frac{133\times 20}{10\times 19}.

$$x=\frac{2660}{190}$$

Divide 2660 by 190 to get 14.

$$x=14$$