In this lesson we will learn:
- Inequalities, plotting inequalities on the number line- Solving inequalities, solving and plotting multi-step inequalities
- Negative inequalities, what happens when you multiply by a negative?
- Two equations with two unknowns, solve for both variables when you have two equations.
- Two equations, no solution, sometimes two equations have no solutions, or many!
x≥1 we can say that: x is greater than or equal to 1, x is at least 1, or x is no less than 1.
x≤ -2 we can say that: x is less than or equal to -2, x is at most -2, or x is no more than -2.
Whenever you multiply or divide an inequality by a negative, flip the inequality sign.
Solving two equations with tow unknowns: first, pick an equation, second solve for one variable in terms of the other, then plug into the second equation and solve for one of the variables. Finally, plug that answer into any of your equation to solve for the second variable.
Solving two equations with no solution, sometimes two equations have no solutions, or many. With two equations and two unknowns, just like for 1 equation with 1 unknown it has three possibilities; there could be exactly one solution, there could be no solution, or there could be many solutions.
Solve of Inequalities can be having infinitely many solutions, it is impossible to presenting in very large list, so we will present in form of sets either graphically on a number line or textually using interval notation.
The compound inequalities represent by the logical “or, ||” are solved by solutions of either inequality, the set is the union of each individual solution set.
The compound inequalities that create the logical “and, &” require that all inequalities are solved by a single solution set and solution set is the intersection of each individual solution.
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