Solve -1/3[-1/2(-1-x)-1/6]-1/12=frac{1}{24}

$$- \frac { 1 } { 3 } [ - \frac { 1 } { 2 } ( - 1 - x ) - \frac { 1 } { 6 } ] - \frac { 1 } { 12 } = \frac { 1 } { 24 }$$

Solve for x

$$x = -\frac{17}{12} = -1\frac{5}{12} \approx -1.416666667$$

Steps for Solving Linear Equation

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

$$-\frac{1}{3}\left(-\frac{1}{2}\left(-1\right)-\frac{1}{2}\left(-1\right)x-\frac{1}{6}\right)-\frac{1}{12}=\frac{1}{24}$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$-\frac{1}{3}\left(\frac{1}{2}-\frac{1}{2}\left(-1\right)x-\frac{1}{6}\right)-\frac{1}{12}=\frac{1}{24}$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$-\frac{1}{3}\left(\frac{1}{2}+\frac{1}{2}x-\frac{1}{6}\right)-\frac{1}{12}=\frac{1}{24}$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$-\frac{1}{3}\left(\frac{3}{6}+\frac{1}{2}x-\frac{1}{6}\right)-\frac{1}{12}=\frac{1}{24}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}\left(\frac{3-1}{6}+\frac{1}{2}x\right)-\frac{1}{12}=\frac{1}{24}$$

Subtract 1 from 3 to get 2.

$$-\frac{1}{3}\left(\frac{2}{6}+\frac{1}{2}x\right)-\frac{1}{12}=\frac{1}{24}$$

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

$$-\frac{1}{3}\left(\frac{1}{3}+\frac{1}{2}x\right)-\frac{1}{12}=\frac{1}{24}$$

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

$$-\frac{1}{3}\times \frac{1}{3}-\frac{1}{3}\times \frac{1}{2}x-\frac{1}{12}=\frac{1}{24}$$

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

$$\frac{-1}{3\times 3}-\frac{1}{3}\times \frac{1}{2}x-\frac{1}{12}=\frac{1}{24}$$

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

$$\frac{-1}{9}-\frac{1}{3}\times \frac{1}{2}x-\frac{1}{12}=\frac{1}{24}$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$-\frac{1}{9}-\frac{1}{3}\times \frac{1}{2}x-\frac{1}{12}=\frac{1}{24}$$

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

$$-\frac{1}{9}+\frac{-1}{3\times 2}x-\frac{1}{12}=\frac{1}{24}$$

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

$$-\frac{1}{9}+\frac{-1}{6}x-\frac{1}{12}=\frac{1}{24}$$

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

$$-\frac{1}{9}-\frac{1}{6}x-\frac{1}{12}=\frac{1}{24}$$

Least common multiple of 9 and 12 is 36. Convert -\frac{1}{9} and \frac{1}{12} to fractions with denominator 36.

$$-\frac{4}{36}-\frac{1}{6}x-\frac{3}{36}=\frac{1}{24}$$

Since -\frac{4}{36} and \frac{3}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-3}{36}-\frac{1}{6}x=\frac{1}{24}$$

Subtract 3 from -4 to get -7.

$$-\frac{7}{36}-\frac{1}{6}x=\frac{1}{24}$$

Add \frac{7}{36} to both sides.

$$-\frac{1}{6}x=\frac{1}{24}+\frac{7}{36}$$

Least common multiple of 24 and 36 is 72. Convert \frac{1}{24} and \frac{7}{36} to fractions with denominator 72.

$$-\frac{1}{6}x=\frac{3}{72}+\frac{14}{72}$$

Since \frac{3}{72} and \frac{14}{72} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}x=\frac{3+14}{72}$$

Add 3 and 14 to get 17.

$$-\frac{1}{6}x=\frac{17}{72}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$x=\frac{17}{72}\left(-6\right)$$

Express \frac{17}{72}\left(-6\right) as a single fraction.

$$x=\frac{17\left(-6\right)}{72}$$

Multiply 17 and -6 to get -102.

$$x=\frac{-102}{72}$$

Reduce the fraction \frac{-102}{72} to lowest terms by extracting and canceling out 6.

$$x=-\frac{17}{12}$$