Solve (11/2-1/3):(-1/6)<10,5:(-2,1)

$$( 1 \frac { 1 } { 2 } - \frac { 1 } { 3 } ) : ( - \frac { 1 } { 6 } ) < 10,5 : ( - 2,1 )$$

Verify

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{\frac{2+1}{2}-\frac{1}{3}}{-\frac{1}{6}}<\frac{10,5}{-2,1}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{2}-\frac{1}{3}}{-\frac{1}{6}}<\frac{10,5}{-2,1}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{9}{6}-\frac{2}{6}}{-\frac{1}{6}}<\frac{10,5}{-2,1}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-2}{6}}{-\frac{1}{6}}<\frac{10,5}{-2,1}$$

Subtract 2 from 9 to get 7.

$$\frac{\frac{7}{6}}{-\frac{1}{6}}<\frac{10,5}{-2,1}$$

Divide \frac{7}{6} by -\frac{1}{6} by multiplying \frac{7}{6} by the reciprocal of -\frac{1}{6}.

$$\frac{7}{6}\left(-6\right)<\frac{10,5}{-2,1}$$

Express \frac{7}{6}\left(-6\right) as a single fraction.

$$\frac{7\left(-6\right)}{6}<\frac{10,5}{-2,1}$$

Multiply 7 and -6 to get -42.

$$\frac{-42}{6}<\frac{10,5}{-2,1}$$

Divide -42 by 6 to get -7.

$$-7<\frac{10,5}{-2,1}$$

Expand \frac{10,5}{-2,1} by multiplying both numerator and the denominator by 10.

$$-7<\frac{105}{-21}$$

Divide 105 by -21 to get -5.

$$-7<-5$$

Compare -7 and -5.

$$\text{true}$$