How do you go from the above step to the next step.utkarshakash said:Homework Statement
[itex]x^2 \geq [x]^2[/itex]
[] denotes Greatest Integer Function
{} denotes Fractional Part
Homework Equations
The Attempt at a Solution
[itex] x^2-[x]^2 \geq 0 \\
(x+[x])(x-[x]) \geq 0 [/itex]
[itex]-[x] \leq x \leq [x] \\
[/itex]
Considering left inequality
[itex]
x \geq -[x] \\
\left\{x\right\} \geq -2[x]
[/itex]
SammyS said:How do you go from the above step to the next step.
(It does look valid, but an explanation seems to be in order.)
An inequality is a mathematical expression that compares two quantities or values. It uses symbols such as <, >, ≤, ≥ to show the relationship between the quantities.
To solve an inequality, you need to follow the same rules as solving an equation. However, if you multiply or divide both sides by a negative number, the inequality sign will flip. You may also need to combine like terms and simplify the expression to find the solution.
The main difference between solving an equation and solving an inequality is that while equations have only one solution, inequalities can have multiple solutions. Additionally, inequalities use different symbols to represent the relationship between quantities, whereas equations use an equal sign (=).
Yes, you can graph an inequality on a number line or on a coordinate plane. The solution set of the inequality will be represented by a shaded region on the graph. The direction of the shading will depend on the inequality symbol used.
To check if your solution to an inequality is correct, you can substitute the value into the original inequality and see if it makes the statement true. If it does, then your solution is correct. You can also graph the inequality and see if the solution falls within the shaded region.