Solve 3/2(x+5)-1/3(x+2)=9/2

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{2} by x+5.

$$\frac{3}{2}x+\frac{3}{2}\times 5-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{3}{2}x+\frac{3\times 5}{2}-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

Multiply 3 and 5 to get 15.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

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

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x-\frac{1}{3}\times 2=\frac{9}{2}$$

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

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x+\frac{-2}{3}=\frac{9}{2}$$

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

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x-\frac{2}{3}=\frac{9}{2}$$

Combine \frac{3}{2}x and -\frac{1}{3}x to get \frac{7}{6}x.

$$\frac{7}{6}x+\frac{15}{2}-\frac{2}{3}=\frac{9}{2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{15}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{7}{6}x+\frac{45}{6}-\frac{4}{6}=\frac{9}{2}$$

Since \frac{45}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}x+\frac{45-4}{6}=\frac{9}{2}$$

Subtract 4 from 45 to get 41.

$$\frac{7}{6}x+\frac{41}{6}=\frac{9}{2}$$

Subtract \frac{41}{6} from both sides.

$$\frac{7}{6}x=\frac{9}{2}-\frac{41}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{9}{2} and \frac{41}{6} to fractions with denominator 6.

$$\frac{7}{6}x=\frac{27}{6}-\frac{41}{6}$$

Since \frac{27}{6} and \frac{41}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}x=\frac{27-41}{6}$$

Subtract 41 from 27 to get -14.

$$\frac{7}{6}x=\frac{-14}{6}$$

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

$$\frac{7}{6}x=-\frac{7}{3}$$

Multiply both sides by \frac{6}{7}, the reciprocal of \frac{7}{6}.

$$x=-\frac{7}{3}\times \frac{6}{7}$$

Multiply -\frac{7}{3} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\times 6}{3\times 7}$$

Do the multiplications in the fraction \frac{-7\times 6}{3\times 7}.

$$x=\frac{-42}{21}$$

Divide -42 by 21 to get -2.

$$x=-2$$