Algebra, Chapter 4, Lesson 5, page 187.
Using Inequalities
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.
- Consecutive numbers are written (remember when?) as `x`, `(x+1)` and `(x+2)` or `3x+3` if we combine like terms.
- Consecutive odd/evens are written as `x`, `(x+2)` and `(x+4)` or `3x+6` if we combine like terms too.
Remember once we have the words translated for our 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 …)
Using the Properties Together
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 are here for Chapter 4-5 as well!