Solve 2x(-3)^-1+sqrt{4/9}-|3-5|

$$2 x ( - 3 ) ^ { - 1 } + \sqrt { \frac { 4 } { 9 } } - | 3 - 5 |$$

Evaluate

$$\frac{-2x-4}{3}$$

Solution Steps

Calculate -3 to the power of -1 and get -\frac{1}{3}.

$$2x\left(-\frac{1}{3}\right)+\sqrt{\frac{4}{9}}-|3-5|$$

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

$$-\frac{2}{3}x+\sqrt{\frac{4}{9}}-|3-5|$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$-\frac{2}{3}x+\frac{2}{3}-|3-5|$$

Subtract 5 from 3 to get -2.

$$-\frac{2}{3}x+\frac{2}{3}-|-2|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$-\frac{2}{3}x+\frac{2}{3}-2$$

Subtract 2 from \frac{2}{3} to get -\frac{4}{3}.

$$-\frac{2}{3}x-\frac{4}{3}$$

Factor

$$\frac{2\left(-x-2\right)}{3}$$

Solution Steps

Calculate -3 to the power of -1 and get -\frac{1}{3}.

$$factor(2x\left(-\frac{1}{3}\right)+\sqrt{\frac{4}{9}}-|3-5|)$$

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

$$factor(-\frac{2}{3}x+\sqrt{\frac{4}{9}}-|3-5|)$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$factor(-\frac{2}{3}x+\frac{2}{3}-|3-5|)$$

Subtract 5 from 3 to get -2.

$$factor(-\frac{2}{3}x+\frac{2}{3}-|-2|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$factor(-\frac{2}{3}x+\frac{2}{3}-2)$$

Subtract 2 from \frac{2}{3} to get -\frac{4}{3}.

$$factor(-\frac{2}{3}x-\frac{4}{3})$$

Factor out \frac{2}{3}.

$$\frac{2\left(-x-2\right)}{3}$$