Day 37 – October 12

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!

 

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