Solve 1/2{1/3[1/4(x-2)-3]-2}-1=x

$$\frac { 1 } { 2 } \{ \frac { 1 } { 3 } [ \frac { 1 } { 4 } ( x - 2 ) - 3 ] - 2 \} - 1 = x$$

Solve for x

$$x = -\frac{62}{23} = -2\frac{16}{23} \approx -2.695652174$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by x-2.

$$\frac{1}{2}\left(\frac{1}{3}\left(\frac{1}{4}x+\frac{1}{4}\left(-2\right)-3\right)-2\right)-1=x$$

Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.

$$\frac{1}{2}\left(\frac{1}{3}\left(\frac{1}{4}x+\frac{-2}{4}-3\right)-2\right)-1=x$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\left(\frac{1}{3}\left(\frac{1}{4}x-\frac{1}{2}-3\right)-2\right)-1=x$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{1}{2}\left(\frac{1}{3}\left(\frac{1}{4}x-\frac{1}{2}-\frac{6}{2}\right)-2\right)-1=x$$

Since -\frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\left(\frac{1}{3}\left(\frac{1}{4}x+\frac{-1-6}{2}\right)-2\right)-1=x$$

Subtract 6 from -1 to get -7.

$$\frac{1}{2}\left(\frac{1}{3}\left(\frac{1}{4}x-\frac{7}{2}\right)-2\right)-1=x$$

Use the distributive property to multiply \frac{1}{3} by \frac{1}{4}x-\frac{7}{2}.

$$\frac{1}{2}\left(\frac{1}{3}\times \frac{1}{4}x+\frac{1}{3}\left(-\frac{7}{2}\right)-2\right)-1=x$$

Multiply \frac{1}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}\left(\frac{1\times 1}{3\times 4}x+\frac{1}{3}\left(-\frac{7}{2}\right)-2\right)-1=x$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 4}.

$$\frac{1}{2}\left(\frac{1}{12}x+\frac{1}{3}\left(-\frac{7}{2}\right)-2\right)-1=x$$

Multiply \frac{1}{3} times -\frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}\left(\frac{1}{12}x+\frac{1\left(-7\right)}{3\times 2}-2\right)-1=x$$

Do the multiplications in the fraction \frac{1\left(-7\right)}{3\times 2}.

$$\frac{1}{2}\left(\frac{1}{12}x+\frac{-7}{6}-2\right)-1=x$$

Fraction \frac{-7}{6} can be rewritten as -\frac{7}{6} by extracting the negative sign.

$$\frac{1}{2}\left(\frac{1}{12}x-\frac{7}{6}-2\right)-1=x$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{1}{2}\left(\frac{1}{12}x-\frac{7}{6}-\frac{12}{6}\right)-1=x$$

Since -\frac{7}{6} and \frac{12}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\left(\frac{1}{12}x+\frac{-7-12}{6}\right)-1=x$$

Subtract 12 from -7 to get -19.

$$\frac{1}{2}\left(\frac{1}{12}x-\frac{19}{6}\right)-1=x$$

Use the distributive property to multiply \frac{1}{2} by \frac{1}{12}x-\frac{19}{6}.

$$\frac{1}{2}\times \frac{1}{12}x+\frac{1}{2}\left(-\frac{19}{6}\right)-1=x$$

Multiply \frac{1}{2} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{2\times 12}x+\frac{1}{2}\left(-\frac{19}{6}\right)-1=x$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 12}.

$$\frac{1}{24}x+\frac{1}{2}\left(-\frac{19}{6}\right)-1=x$$

Multiply \frac{1}{2} times -\frac{19}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{24}x+\frac{1\left(-19\right)}{2\times 6}-1=x$$

Do the multiplications in the fraction \frac{1\left(-19\right)}{2\times 6}.

$$\frac{1}{24}x+\frac{-19}{12}-1=x$$

Fraction \frac{-19}{12} can be rewritten as -\frac{19}{12} by extracting the negative sign.

$$\frac{1}{24}x-\frac{19}{12}-1=x$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{1}{24}x-\frac{19}{12}-\frac{12}{12}=x$$

Since -\frac{19}{12} and \frac{12}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{24}x+\frac{-19-12}{12}=x$$

Subtract 12 from -19 to get -31.

$$\frac{1}{24}x-\frac{31}{12}=x$$

Subtract x from both sides.

$$\frac{1}{24}x-\frac{31}{12}-x=0$$

Combine \frac{1}{24}x and -x to get -\frac{23}{24}x.

$$-\frac{23}{24}x-\frac{31}{12}=0$$

Add \frac{31}{12} to both sides. Anything plus zero gives itself.

$$-\frac{23}{24}x=\frac{31}{12}$$

Multiply both sides by -\frac{24}{23}, the reciprocal of -\frac{23}{24}.

$$x=\frac{31}{12}\left(-\frac{24}{23}\right)$$

Multiply \frac{31}{12} times -\frac{24}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{31\left(-24\right)}{12\times 23}$$

Do the multiplications in the fraction \frac{31\left(-24\right)}{12\times 23}.

$$x=\frac{-744}{276}$$

Reduce the fraction \frac{-744}{276} to lowest terms by extracting and canceling out 12.

$$x=-\frac{62}{23}$$