Types of Inequalities

Find the solution of $ax\le 1$.

Write the set of values of $x$ satisfying the inequation $\sqrt[3]{(x-4)\left(x-7\right)}\ge 2^{\frac{2}{3}}$.

Define strict inequality. Find the solution of $x-2<7$.

Define strict inequality. Find the solution of $x-2>7$.

Define strict inequality. Find the solution of $x+5>9$.

Define strict inequality. Find the solution of $x+3>6$.

Define strict inequality. Find the solution of $x+2>4$.

Define slack inequality. Find the solution of $x-3\ge 6$.

Define slack inequality. Find the solution of $x-5\ge 9$.

Define slack inequality. Find the solution of $x+5\ge 9$.

Define slack inequality. Find the solution of $x+3\ge 6$.

Define slack inequality. Find the solution of $x+2\ge 4$.

Given that $x>y$. Fill in the blank with suitable inequality sign.

If $x^2+9=6x$, find the value of $\sqrt{x}+\frac{1}{\sqrt{x}}$.

Find which option is correct.

$$\begin{gathered} x^2-3x-4=0 \\ {y}^2+4y+3=0 \end{gathered}$$

Find the option which is true.

$$\begin{gathered} 4x^2-4x-3=0 \\ 4y^2+4y-3=0 \end{gathered}$$

Direction : In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
Quantity I: x, such that $12x^2-5x-3=0$
Quantity II: $\mathrm{y},$ such that $3y^2-11y+6=0$

Direction : In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.

Quantity I: $x,$ such that $12x^2-5x-3=0$
Quantity II: $y$, such that $3y^2-11y+6=0$

Direction : In these questions, a relationship between different elements is shown in the statement(s). The statements are followed by Some conclusions. Give answer

Statements:
J  ≥  A > D = E; L < A < M
Conclusions:
I. M < J
II. J > L
III. D > L
IV. E < M

Write the solution set of $\left|x+\frac{1}{x}\right|>2$.