Inequalities Quiz 1

Question 1

Find the value of $$x$$ for $${\log _3}(x - 1) < {\log _9}(x - 1)$$

Accepted Answer

$$(2,\infty )$$

Answer

$$( - \infty ,2)$$

Answer

$$( - 2,2)$$

Answer

$$( - 1,1)$$

Question 2

Solve for $$x$$ when $${\log _{\dfrac{1}{3}}}(4x) > {\log _{\dfrac{1}{3}}}(2x + 3)$$

Accepted Answer

$$\left( {0,\dfrac{3}{2}} \right)$$

Answer

$$\left( {\dfrac{{ - 3}}{2},\dfrac{3}{2}} \right)$$

Answer

$$\left( {\dfrac{{ - 3}}{2},0} \right)$$

Answer

$$\dfrac{{ - 3}}{2},\dfrac{3}{2}$$

Question 3

Find the equation $$\dfrac{{3x - 4}}{4} > \dfrac{{x + 1}}{2} - 1$$

Accepted Answer

$$x > 2$$

Answer

$$x < 2$$

Answer

$$x < 1$$

Answer

$$x > 4$$

Question 4

Find the given equation $$\dfrac{1}{3}\left( {\dfrac{{3x}}{5} + 12} \right) > \dfrac{1}{2}\left( {x + 6} \right)$$

Accepted Answer

$$ - \infty ,\dfrac{{10}}{3}$$

Answer

$$\infty ,\dfrac{3}{{10}}$$

Answer

$$ - \infty ,\dfrac{2}{3}$$

Answer

$$\dfrac{2}{3},\infty $$

Question 5

Find the given equation $$\dfrac{{{x^2} - 1}}{{{x^2} - 5x + 6}} > 1$$

Accepted Answer

$$\left( {\dfrac{7}{5},2} \right) \cup \left( {3,\infty } \right)$$

Answer

$$\left( {\dfrac{7}{5},2} \right) \cap \left( {5,\infty } \right)$$

Answer

$$\left( {\dfrac{5}{7},3} \right) \cap \left( {3,\infty } \right)$$

Answer

$$\left( {\dfrac{5}{7},7} \right) \cup \left( {1,\infty } \right)$$