Day 81 and 82 – January 6, 7

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!

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