Solve x(-5/3)-16/21leq17/14

$$x ( - \frac { 5 } { 3 } ) - \frac { 16 } { 21 } \leq \frac { 17 } { 14 }$$

Solve for x

$$x\geq -\frac{83}{70}$$

Solution Steps

Add \frac{16}{21} to both sides.

$$x\left(-\frac{5}{3}\right)\leq \frac{17}{14}+\frac{16}{21}$$

Least common multiple of 14 and 21 is 42. Convert \frac{17}{14} and \frac{16}{21} to fractions with denominator 42.

$$x\left(-\frac{5}{3}\right)\leq \frac{51}{42}+\frac{32}{42}$$

Since \frac{51}{42} and \frac{32}{42} have the same denominator, add them by adding their numerators.

$$x\left(-\frac{5}{3}\right)\leq \frac{51+32}{42}$$

Add 51 and 32 to get 83.

$$x\left(-\frac{5}{3}\right)\leq \frac{83}{42}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}. Since -\frac{5}{3} is negative, the inequality direction is changed.

$$x\geq \frac{83}{42}\left(-\frac{3}{5}\right)$$

Multiply \frac{83}{42} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{83\left(-3\right)}{42\times 5}$$

Do the multiplications in the fraction \frac{83\left(-3\right)}{42\times 5}.

$$x\geq \frac{-249}{210}$$

Reduce the fraction \frac{-249}{210} to lowest terms by extracting and canceling out 3.

$$x\geq -\frac{83}{70}$$