Solve 1/2x+1/3(x+5)+1/4(x+5)=3

$$\frac { 1 } { 2 } x + \frac { 1 } { 3 } ( x + 5 ) + \frac { 1 } { 4 } ( x + 5 ) = 3$$

Solve for x

$$x=\frac{1}{13}\approx 0.076923077$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x+5.

$$\frac{1}{2}x+\frac{1}{3}x+\frac{1}{3}\times 5+\frac{1}{4}\left(x+5\right)=3$$

Multiply \frac{1}{3} and 5 to get \frac{5}{3}.

$$\frac{1}{2}x+\frac{1}{3}x+\frac{5}{3}+\frac{1}{4}\left(x+5\right)=3$$

Combine \frac{1}{2}x and \frac{1}{3}x to get \frac{5}{6}x.

$$\frac{5}{6}x+\frac{5}{3}+\frac{1}{4}\left(x+5\right)=3$$

Use the distributive property to multiply \frac{1}{4} by x+5.

$$\frac{5}{6}x+\frac{5}{3}+\frac{1}{4}x+\frac{1}{4}\times 5=3$$

Multiply \frac{1}{4} and 5 to get \frac{5}{4}.

$$\frac{5}{6}x+\frac{5}{3}+\frac{1}{4}x+\frac{5}{4}=3$$

Combine \frac{5}{6}x and \frac{1}{4}x to get \frac{13}{12}x.

$$\frac{13}{12}x+\frac{5}{3}+\frac{5}{4}=3$$

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{13}{12}x+\frac{20}{12}+\frac{15}{12}=3$$

Since \frac{20}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{13}{12}x+\frac{20+15}{12}=3$$

Add 20 and 15 to get 35.

$$\frac{13}{12}x+\frac{35}{12}=3$$

Subtract \frac{35}{12} from both sides.

$$\frac{13}{12}x=3-\frac{35}{12}$$

Convert 3 to fraction \frac{36}{12}.

$$\frac{13}{12}x=\frac{36}{12}-\frac{35}{12}$$

Since \frac{36}{12} and \frac{35}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{12}x=\frac{36-35}{12}$$

Subtract 35 from 36 to get 1.

$$\frac{13}{12}x=\frac{1}{12}$$

Multiply both sides by \frac{12}{13}, the reciprocal of \frac{13}{12}.

$$x=\frac{1}{12}\times \frac{12}{13}$$

Multiply \frac{1}{12} times \frac{12}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 12}{12\times 13}$$

Cancel out 12 in both numerator and denominator.

$$x=\frac{1}{13}$$