Algebra: Chapter 4, Lesson 4, page 183 and Lesson 5, page 187.
Using the Properties Together (Lesson 4)
Inequalities of 2 steps
We do the same, again, as equalities and solve by:
- Distributing when required
- Combining like terms
- Adding or subtracting terms to isolate variables and numbers (constants)
- Multiplying or dividing to finish solving for the variable, remembering to reverse the sign of the inequality IF we multiply or divide by a NEGATIVE NUMBER.
For example:
`7x + 4 ≤ 4x + 16`
subtract `4x` from both sides, that looks like
`7x – 4x + 4 ≤ 4x – 4x + 16`
now combine like terms on the left and the right sides
`3x + 4 ≤ 16`
subtract 4 from each side
`3x + 4 – 4 ≤ 16 – 4`
combine like terms again on both sides, so that
`3x ≤ 12`
and finally divide both sides by 3
`(3x)/3 ≤ 12/3`, so that finally
`x ≤ 4`
Go slow and show all the steps! Here are some more examples from purplemath.com
Two of tonight’s homework problems for Lesson 4 solved by MrE are here! Just click it!
Using Inequalities (Lesson 5)
We learned key phrases for lesson 5 (word translation problems):
- “Less than or equal to”, “is at most”, “no more than” — ≤
- “No less than”, “at least”, “more than or equal to” — ≥
- “Is less than” — <
- “Is greater than” — >
We learned to read the problem, draw a picture or understand what is being asked of us before we start solving an equation or inequality.
Remember for 2 step inequalities, we do the same, again, as equalities and solve by:
- Distributing when required
- Combining like terms
- Adding or subtracting terms to isolate variables and numbers (constants)
- Multiplying or dividing to finish solving for the variable, remembering to reverse the sign of the inequality IF we multiply or divide by a NEGATIVE NUMBER.
Here are some keyword descriptions from purplemath.com to help us with word problems (ugh …)
Two of tonight’s Lesson 5 homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 2, Lesson 8, page 93.
Inverse of a Sum and Simplifying
The inverse of a SUM Property: For any rational numbers, `−(a+b)=−a+(−b)`. The additive inverse of a sum is the sum of the additive inverses.
In other words, if you have a `−` in front of a paranthesis, then just change the sign of EVERYTHING inside.
For example: `−(2a−7b−6)` becomes the opposite of each term, `−2a+7b+6`.
Another example: `3y-2-(2y-4)=3y-2-2y+4`. Combining like terms, we see the answer `=2y-4`
Two of tonight’s homework problems solved by MrE are here! Just click it!