Solve x+4-4/3=3/2-4-x

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

Solve for x

$$x = -\frac{31}{12} = -2\frac{7}{12} \approx -2.583333333$$

Steps for Solving Linear Equation

Convert 4 to fraction \frac{12}{3}.

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

Since \frac{12}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 12 to get 8.

$$x+\frac{8}{3}=\frac{3}{2}-4-x$$

Convert 4 to fraction \frac{8}{2}.

$$x+\frac{8}{3}=\frac{3}{2}-\frac{8}{2}-x$$

Since \frac{3}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{8}{3}=\frac{3-8}{2}-x$$

Subtract 8 from 3 to get -5.

$$x+\frac{8}{3}=-\frac{5}{2}-x$$

Add x to both sides.

$$x+\frac{8}{3}+x=-\frac{5}{2}$$

Combine x and x to get 2x.

$$2x+\frac{8}{3}=-\frac{5}{2}$$

Subtract \frac{8}{3} from both sides.

$$2x=-\frac{5}{2}-\frac{8}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{5}{2} and \frac{8}{3} to fractions with denominator 6.

$$2x=-\frac{15}{6}-\frac{16}{6}$$

Since -\frac{15}{6} and \frac{16}{6} have the same denominator, subtract them by subtracting their numerators.

$$2x=\frac{-15-16}{6}$$

Subtract 16 from -15 to get -31.

$$2x=-\frac{31}{6}$$

Divide both sides by 2.

$$x=\frac{-\frac{31}{6}}{2}$$

Express \frac{-\frac{31}{6}}{2} as a single fraction.

$$x=\frac{-31}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$x=\frac{-31}{12}$$

Fraction \frac{-31}{12} can be rewritten as -\frac{31}{12} by extracting the negative sign.

$$x=-\frac{31}{12}$$