Algebra: Chapter 4, Lesson 2, page 175 and Lesson 3, page 180.
The Addition Property of Inequalities
Don’t forget, the equations:
- if `a < b`, then `a + c < b + c`
- if `a > b`, then `a + c > b + c`
and similar statements are true for ≤ and ≥
For inequality of one step, follow the EXACT same steps as equalities. The only things we have to remember when graphing on a number line:
- For the symbols ≤ and ≥, the circle must be CLOSED because we INCLUDE the data point
- For the symbols < and >, the circle must be OPEN because we get as close as possible to the data point but it is NOT INCLUDED!
Here is a link from PURPLEMATH.com with some more examples!
The Multiplication Property of Inequalities
The property states if `c` is POSITIVE
- if `a < b`, then `ac < bc` and
- if `a > b`, then `ac > bc`
Where `c` is NEGATIVE
- if `a < b`, then `ac > bc` and
- if `a > b`, then `ac < bc`
Following the EXACT same steps as equalities, we have learned to solve 1 step equations with inequalities. The ONLY difference is when multiplying or dividing by a NEGATIVE number, we must REVERSE the sign of the inequality for the final solution!! If we divide or multiply by a positive number, we leave the inequality sign alone.
Here are some examples from purplemath.com that have to do with inequalities with products and divisions.
Two of tonight’s homework problems for Chapter 4-2 are solved by MrE are here! Just click it! Two more are here for Chapter 4-3 as well!
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Algebra 1a: Chapter 2, Lesson 7, page 89.
Using the Distributive Property
The distributive property of multiplication over addition and subtraction is:
`a(b+c)=ab+ac` and `a(b−c)=ab−ac`
You can also combine LIKE TERMS ONLY IF THE VARIABLE AND THE EXPONENT OF THE VARIABLE ARE EXACTLY THE SAME!
Examples, (remember to use the wacky arrows!):
`9(x – 5) = 9x – 9(5) = 9x – 45`
`-4(x – 2y + 3z) = -4x +(-4)(-2y) + (-4)(3z) = -4x -4(-2y) -4(3z)`
`= -4x + 8y – 12z`
(if it comes up, don’t forget the change-change or bling-bling, double negative thingy …)
Here is a link from purplemath.com about the distributive property with more examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!