Solve {l}{1/3+1/2+1/a=4}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { \frac{1}{3} + \frac{1}{2} + \frac{1}{a} = 4 }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for a, b, c

$$c=\frac{6}{19}\approx 0.315789474$$

Solution Steps

Consider the first equation. Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6a, the least common multiple of 3,2,a.

$$6a\times \frac{1}{3}+6a\times \frac{1}{2}+6=24a$$

Multiply 6 and \frac{1}{3} to get 2.

$$2a+6a\times \frac{1}{2}+6=24a$$

Multiply 6 and \frac{1}{2} to get 3.

$$2a+3a+6=24a$$

Combine 2a and 3a to get 5a.

$$5a+6=24a$$

Subtract 24a from both sides.

$$5a+6-24a=0$$

Combine 5a and -24a to get -19a.

$$-19a+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-19a=-6$$

Divide both sides by -19.

$$a=\frac{-6}{-19}$$

Fraction \frac{-6}{-19} can be simplified to \frac{6}{19} by removing the negative sign from both the numerator and the denominator.

$$a=\frac{6}{19}$$

Consider the second equation. Insert the known values of variables into the equation.

$$b=\frac{6}{19}$$

Consider the third equation. Insert the known values of variables into the equation.

$$c=\frac{6}{19}$$

The system is now solved.

$$a=\frac{6}{19} b=\frac{6}{19} c=\frac{6}{19}$$