Solve 3/4(x+1)-8/3=9/2-7/6(2x+3)

$$3 / 4 ( x + 1 ) - 8 / 3 = 9 / 2 - 7 / 6 ( 2 x + 3 )$$

Solve for x

$$x=\frac{35}{37}\approx 0.945945946$$

Steps for Solving Linear Equation

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

$$\frac{3}{4}x+\frac{3}{4}-\frac{8}{3}=\frac{9}{2}-\frac{7}{6}\left(2x+3\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{8}{3} to fractions with denominator 12.

$$\frac{3}{4}x+\frac{9}{12}-\frac{32}{12}=\frac{9}{2}-\frac{7}{6}\left(2x+3\right)$$

Since \frac{9}{12} and \frac{32}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}x+\frac{9-32}{12}=\frac{9}{2}-\frac{7}{6}\left(2x+3\right)$$

Subtract 32 from 9 to get -23.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}-\frac{7}{6}\left(2x+3\right)$$

Use the distributive property to multiply -\frac{7}{6} by 2x+3.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}-\frac{7}{6}\times 2x-\frac{7}{6}\times 3$$

Express -\frac{7}{6}\times 2 as a single fraction.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}+\frac{-7\times 2}{6}x-\frac{7}{6}\times 3$$

Multiply -7 and 2 to get -14.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}+\frac{-14}{6}x-\frac{7}{6}\times 3$$

Reduce the fraction \frac{-14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}-\frac{7}{3}x-\frac{7}{6}\times 3$$

Express -\frac{7}{6}\times 3 as a single fraction.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}-\frac{7}{3}x+\frac{-7\times 3}{6}$$

Multiply -7 and 3 to get -21.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}-\frac{7}{3}x+\frac{-21}{6}$$

Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9}{2}-\frac{7}{3}x-\frac{7}{2}$$

Since \frac{9}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}x-\frac{23}{12}=\frac{9-7}{2}-\frac{7}{3}x$$

Subtract 7 from 9 to get 2.

$$\frac{3}{4}x-\frac{23}{12}=\frac{2}{2}-\frac{7}{3}x$$

Divide 2 by 2 to get 1.

$$\frac{3}{4}x-\frac{23}{12}=1-\frac{7}{3}x$$

Add \frac{7}{3}x to both sides.

$$\frac{3}{4}x-\frac{23}{12}+\frac{7}{3}x=1$$

Combine \frac{3}{4}x and \frac{7}{3}x to get \frac{37}{12}x.

$$\frac{37}{12}x-\frac{23}{12}=1$$

Add \frac{23}{12} to both sides.

$$\frac{37}{12}x=1+\frac{23}{12}$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{37}{12}x=\frac{12}{12}+\frac{23}{12}$$

Since \frac{12}{12} and \frac{23}{12} have the same denominator, add them by adding their numerators.

$$\frac{37}{12}x=\frac{12+23}{12}$$

Add 12 and 23 to get 35.

$$\frac{37}{12}x=\frac{35}{12}$$

Multiply both sides by \frac{12}{37}, the reciprocal of \frac{37}{12}.

$$x=\frac{35}{12}\times \frac{12}{37}$$

Multiply \frac{35}{12} times \frac{12}{37} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{35\times 12}{12\times 37}$$

Cancel out 12 in both numerator and denominator.

$$x=\frac{35}{37}$$