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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply \frac{1}{4} by x+3.

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

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

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

Combine \frac{1}{2}x and \frac{1}{4}x to get \frac{3}{4}x.

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

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

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

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

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

Use the distributive property to multiply -\frac{1}{3} by x+2.

$$\frac{3}{4}x+\frac{5}{4}=3-\frac{1}{3}x-\frac{1}{3}\times 2$$

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Convert 3 to fraction \frac{9}{3}.

$$\frac{3}{4}x+\frac{5}{4}=\frac{9}{3}-\frac{1}{3}x-\frac{2}{3}$$

Since \frac{9}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}x+\frac{5}{4}=\frac{9-2}{3}-\frac{1}{3}x$$

Subtract 2 from 9 to get 7.

$$\frac{3}{4}x+\frac{5}{4}=\frac{7}{3}-\frac{1}{3}x$$

Add \frac{1}{3}x to both sides.

$$\frac{3}{4}x+\frac{5}{4}+\frac{1}{3}x=\frac{7}{3}$$

Combine \frac{3}{4}x and \frac{1}{3}x to get \frac{13}{12}x.

$$\frac{13}{12}x+\frac{5}{4}=\frac{7}{3}$$

Subtract \frac{5}{4} from both sides.

$$\frac{13}{12}x=\frac{7}{3}-\frac{5}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{7}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{13}{12}x=\frac{28}{12}-\frac{15}{12}$$

Since \frac{28}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{12}x=\frac{28-15}{12}$$

Subtract 15 from 28 to get 13.

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

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

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

Cancel out \frac{13}{12} and its reciprocal \frac{12}{13}.

$$x=1$$