Solving inequalities Quiz 1

Question 1

Solve the given inequality: $$\left| {\left( {x + \dfrac{2}{3}} \right)} \right| > \dfrac{5}{3}$$

Accepted Answer

$$x \in \left( { - \dfrac{7}{3},1} \right)$$

Answer

$$x \in \left[ { - \dfrac{7}{3},1} \right)$$

Answer

$$x \in \left[ { - \dfrac{7}{3},1} \right]$$

Answer

$$x \in \left[ {1, + \infty } \right]$$

Question 2

Solve the given inequality for value of $$x: \sin x\cos x > 0$$

Accepted Answer

$$x \in (0,\dfrac{\pi }{4})$$

Answer

$$x \in \{ \Phi \} $$

Answer

$$x \in (0,\dfrac{\pi }{2})$$

Answer

$$x \in (\dfrac{\pi }{2},\dfrac{\pi }{4})$$

Question 3

Find pairs of all consecutive even positive integers such that they are smaller than $$24$$ and their sum is more than $$28$$ .

Accepted Answer

$$(14,16), (16,18) \& (18,20)$$

Answer

$$(16,18), (18,20) \& (20,22)$$

Answer

$$(16,18), (18,20)$$

Answer

$$(14,16), (16,18)$$

Question 4

The cost and revenue functions of a product are given by $$f\left( x ight){	ext{ }} = {	ext{ }}x + 100$$and $$g\left( x ight){	ext{ }} = {	ext{ }}2x{	ext{ }} + 20$$ respectively, where  $$x$$ is the number of items produced by the manufacturer. How many items should the shopkeeper sell such that he earns a bit of profit?

Accepted Answer

$$81$$

Answer

$$80$$

Answer

$$82$$

Answer

$$79$$

Question 5

If $$ - 2 < x < 2$$ then find the values of $$a$$ and $$b$$ in: $$a < 2x + 4 \leqslant b + 4$$

Accepted Answer

$$a = 0,b = 4$$

Answer

$$a = 2,b = 4$$

Answer

$$a = 4,b = 0$$

Answer

$$a = 4,b = 2$$