Solve {1/3[1/4(1/5x-2)-2]-2}-2=0

$$\{ \frac { 1 } { 3 } [ \frac { 1 } { 4 } ( \frac { 1 } { 5 } x - 2 ) - 2 ] - 2 \} - 2 = 0$$

Solve for x

$$x=290$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by \frac{1}{5}x-2.

$$\frac{1}{3}\left(\frac{1}{4}\times \frac{1}{5}x+\frac{1}{4}\left(-2\right)-2\right)-2-2=0$$

Multiply \frac{1}{4} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}\left(\frac{1\times 1}{4\times 5}x+\frac{1}{4}\left(-2\right)-2\right)-2-2=0$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 5}.

$$\frac{1}{3}\left(\frac{1}{20}x+\frac{1}{4}\left(-2\right)-2\right)-2-2=0$$

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

$$\frac{1}{3}\left(\frac{1}{20}x+\frac{-2}{4}-2\right)-2-2=0$$

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

$$\frac{1}{3}\left(\frac{1}{20}x-\frac{1}{2}-2\right)-2-2=0$$

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

$$\frac{1}{3}\left(\frac{1}{20}x-\frac{1}{2}-\frac{4}{2}\right)-2-2=0$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\left(\frac{1}{20}x+\frac{-1-4}{2}\right)-2-2=0$$

Subtract 4 from -1 to get -5.

$$\frac{1}{3}\left(\frac{1}{20}x-\frac{5}{2}\right)-2-2=0$$

Use the distributive property to multiply \frac{1}{3} by \frac{1}{20}x-\frac{5}{2}.

$$\frac{1}{3}\times \frac{1}{20}x+\frac{1}{3}\left(-\frac{5}{2}\right)-2-2=0$$

Multiply \frac{1}{3} times \frac{1}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{3\times 20}x+\frac{1}{3}\left(-\frac{5}{2}\right)-2-2=0$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 20}.

$$\frac{1}{60}x+\frac{1}{3}\left(-\frac{5}{2}\right)-2-2=0$$

Multiply \frac{1}{3} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{60}x+\frac{1\left(-5\right)}{3\times 2}-2-2=0$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{3\times 2}.

$$\frac{1}{60}x+\frac{-5}{6}-2-2=0$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$\frac{1}{60}x-\frac{5}{6}-2-2=0$$

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

$$\frac{1}{60}x-\frac{5}{6}-\frac{12}{6}-2=0$$

Since -\frac{5}{6} and \frac{12}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{60}x+\frac{-5-12}{6}-2=0$$

Subtract 12 from -5 to get -17.

$$\frac{1}{60}x-\frac{17}{6}-2=0$$

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

$$\frac{1}{60}x-\frac{17}{6}-\frac{12}{6}=0$$

Since -\frac{17}{6} and \frac{12}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{60}x+\frac{-17-12}{6}=0$$

Subtract 12 from -17 to get -29.

$$\frac{1}{60}x-\frac{29}{6}=0$$

Add \frac{29}{6} to both sides. Anything plus zero gives itself.

$$\frac{1}{60}x=\frac{29}{6}$$

Multiply both sides by 60, the reciprocal of \frac{1}{60}.

$$x=\frac{29}{6}\times 60$$

Express \frac{29}{6}\times 60 as a single fraction.

$$x=\frac{29\times 60}{6}$$

Multiply 29 and 60 to get 1740.

$$x=\frac{1740}{6}$$

Divide 1740 by 6 to get 290.

$$x=290$$