Solve -6=1/6+16/3+c

$$-6 = \frac{ 1 }{ 6 } + \frac{ 16 }{ 3 } +c$$

Solve for c

$$c = -\frac{23}{2} = -11\frac{1}{2} = -11.5$$

Steps for Solving Linear Equation

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{16}{3} to fractions with denominator 6.

$$-6=\frac{1}{6}+\frac{32}{6}+c$$

Since \frac{1}{6} and \frac{32}{6} have the same denominator, add them by adding their numerators.

$$-6=\frac{1+32}{6}+c$$

Add 1 and 32 to get 33.

$$-6=\frac{33}{6}+c$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$-6=\frac{11}{2}+c$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{11}{2}+c=-6$$

Subtract \frac{11}{2} from both sides.

$$c=-6-\frac{11}{2}$$

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

$$c=-\frac{12}{2}-\frac{11}{2}$$

Since -\frac{12}{2} and \frac{11}{2} have the same denominator, subtract them by subtracting their numerators.

$$c=\frac{-12-11}{2}$$

Subtract 11 from -12 to get -23.

$$c=-\frac{23}{2}$$