Today we talked about Inequalities.
An Inequality is whether (or not) the left side equals the right side.
Inequality Symbols:
> less than
< greater than
≤ less than or equal to
≥ greater than or equal to
≠ not equal to
≈ approximately equal to
You CAN NOT include ∞ (infinity) because it never ends.
As an example, JoJo showed that Hana's height (5'3") is less than Christine's height (5'7")
Hana's height < Christine's height
But if Hana's height ≤ Christine's height
Hana could be 5'6" if the inequality were true
Solve for x:
4x - 5 ≥ 13
Add 5 to both sides
4x + 0 ≥ 18
4x ≥ 18
Divide 4 from both sides
4x/4 ≥ 18/4
x ≥ 9/2 Interval notation
•-----|----|----|--> Number line
9/2 5 6 7
[9/2, ∞)
^ ^ not included
included } Set notation
Don't forget to CHECK!
4(5) - 5 ≥ 13
20 - 5 ≥ 13
15 ≥ 13 Yes, the inequality is true.
We don't have any homework over the break.
The next scribe will be Danielle.
Steps to Solving a Linear Inequality
ReplyDelete1. Simplify each side separately.Clear parentheses by using distributive property and combine like terms
2. Isolate the variable terms on one side. Use the addition property of equality , getting all terms with variables on one side of the inequality and on the other side, all numbers.
3. Isolate the variable. By using the multiplication property of inequality, change the inequality to the form xk