Solve (x-1/3)*1/2-4/5=-1

$$( x - \frac { 1 } { 3 } ) \cdot \frac { 1 } { 2 } - \frac { 4 } { 5 } = - 1$$

Solve for x

$$x=-\frac{1}{15}\approx -0.066666667$$

Steps for Solving Linear Equation

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

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

Multiply -\frac{1}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-1}{3\times 2}.

$$x\times \frac{1}{2}+\frac{-1}{6}-\frac{4}{5}=-1$$

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

$$x\times \frac{1}{2}-\frac{1}{6}-\frac{4}{5}=-1$$

Least common multiple of 6 and 5 is 30. Convert -\frac{1}{6} and \frac{4}{5} to fractions with denominator 30.

$$x\times \frac{1}{2}-\frac{5}{30}-\frac{24}{30}=-1$$

Since -\frac{5}{30} and \frac{24}{30} have the same denominator, subtract them by subtracting their numerators.

$$x\times \frac{1}{2}+\frac{-5-24}{30}=-1$$

Subtract 24 from -5 to get -29.

$$x\times \frac{1}{2}-\frac{29}{30}=-1$$

Add \frac{29}{30} to both sides.

$$x\times \frac{1}{2}=-1+\frac{29}{30}$$

Convert -1 to fraction -\frac{30}{30}.

$$x\times \frac{1}{2}=-\frac{30}{30}+\frac{29}{30}$$

Since -\frac{30}{30} and \frac{29}{30} have the same denominator, add them by adding their numerators.

$$x\times \frac{1}{2}=\frac{-30+29}{30}$$

Add -30 and 29 to get -1.

$$x\times \frac{1}{2}=-\frac{1}{30}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=-\frac{1}{30}\times 2$$

Express -\frac{1}{30}\times 2 as a single fraction.

$$x=\frac{-2}{30}$$

Reduce the fraction \frac{-2}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{15}$$