Solve 4x-3-(-4-6/5)-x=-3x+2/3

$$4x-3-(-4- \frac{ 6 }{ 5 } )-x=-3x+ \frac{ 2 }{ 3 }$$

Solve for x

$$x=-\frac{23}{90}\approx -0.255555556$$

Steps for Solving Linear Equation

Convert -4 to fraction -\frac{20}{5}.

$$4x-3-\left(-\frac{20}{5}-\frac{6}{5}\right)-x=-3x+\frac{2}{3}$$

Since -\frac{20}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$4x-3-\frac{-20-6}{5}-x=-3x+\frac{2}{3}$$

Subtract 6 from -20 to get -26.

$$4x-3-\left(-\frac{26}{5}\right)-x=-3x+\frac{2}{3}$$

The opposite of -\frac{26}{5} is \frac{26}{5}.

$$4x-3+\frac{26}{5}-x=-3x+\frac{2}{3}$$

Convert -3 to fraction -\frac{15}{5}.

$$4x-\frac{15}{5}+\frac{26}{5}-x=-3x+\frac{2}{3}$$

Since -\frac{15}{5} and \frac{26}{5} have the same denominator, add them by adding their numerators.

$$4x+\frac{-15+26}{5}-x=-3x+\frac{2}{3}$$

Add -15 and 26 to get 11.

$$4x+\frac{11}{5}-x=-3x+\frac{2}{3}$$

Combine 4x and -x to get 3x.

$$3x+\frac{11}{5}=-3x+\frac{2}{3}$$

Add 3x to both sides.

$$3x+\frac{11}{5}+3x=\frac{2}{3}$$

Combine 3x and 3x to get 6x.

$$6x+\frac{11}{5}=\frac{2}{3}$$

Subtract \frac{11}{5} from both sides.

$$6x=\frac{2}{3}-\frac{11}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{11}{5} to fractions with denominator 15.

$$6x=\frac{10}{15}-\frac{33}{15}$$

Since \frac{10}{15} and \frac{33}{15} have the same denominator, subtract them by subtracting their numerators.

$$6x=\frac{10-33}{15}$$

Subtract 33 from 10 to get -23.

$$6x=-\frac{23}{15}$$

Divide both sides by 6.

$$x=\frac{-\frac{23}{15}}{6}$$

Express \frac{-\frac{23}{15}}{6} as a single fraction.

$$x=\frac{-23}{15\times 6}$$

Multiply 15 and 6 to get 90.

$$x=\frac{-23}{90}$$

Fraction \frac{-23}{90} can be rewritten as -\frac{23}{90} by extracting the negative sign.

$$x=-\frac{23}{90}$$