MrE's Algebra Blog

SNOW DAY #1

Algebra 1a: Chapter 4, Lesson 3, page 180.

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 are here for Chapter 4-3!

Algebra 1a: Chapter 4, Lesson 2, page 175.

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!

Two of tonight’s homework problems for Chapter 4-2 are solved by MrE are here! Just click it!

Algebra 1a: Chapter 4, Lesson 1, page 172.

Inequalities and Their Graphs

Symbols:

• `<`, is less than
• `≤`, is less than or equal to
• `>`, is greater than
• `≥`, is greater than or equal to

Open or closed circles on the number line:

• OPEN CIRCLE  (get as close to the value BUT don’t touch) it for `<` or `>`
• CLOSED CIRCLE (included the value on the number line) for `≤` or `≥`

Algebra 1a BENCHMARK #3

Algebra 1a: Chapter 1, 2 and 3 Review

Benchmark #3 Preparation

Chapter Assessment, page 168-169, problems 1-37 ALL

Evening tutoring will be on tonight and tormorrow (Wednesday) of this week in preparation for the Chapter 1 through 3 BENCHMARK #3!

Make sure that your notes are up-to-date.

Know how to:

• Evaluate an algebraic expression
• Order of Operations
• Commututive and Associative Properties
• Exponential Notation
• Evaluate formulas
• Additive inverse
• Distribute (whacky arrows)
• Add/Subtract/Multiply/Divide rational numbers
• Addition property of equalitiy
• Multiplication property of equality
• Remember how to do the whickity-whack divide thingy.

Remember too, the steps to SOLVING 2-STEP EQUATIONS:

1. Multiply both sides to clear fractions or decimals, if necessary.
2. Collect like terms on each side, if necessary.
3. Use the addition property to move the variable to one side and all other terms to the other side of the equation.
4. Collect like terms again, if necessary
5. Add or subtract to isolate the variable and finally
6. Use the multiplication or division or reciprocal properties to solve for the variable.

Algebra 1a: Chapter 3 Review

Skills Practice 8 and 9, pages 16 and 17.

Evening tutoring will be on Tuesday and Wednesday of this week in preparation for the Chapter 1 through 3 BENCHMARK #3!

Make sure that your notes are up-to-date.

Bring your problems worked out and your questions for the Chapter 3 review. These type of questions will appear on the test. Make sure that your notes are up-to-date. Practice makes perfect

Remember how to do the whickity-whack divide thingy.

Remember too, the steps to SOLVING 2-STEP EQUATIONS:

1. Multiply both sides to clear fractions or decimals, if necessary.
2. Collect like terms on each side, if necessary.
3. Use the addition property to move the variable to one side and all other terms to the other side of the equation.
4. Collect like terms again, if necessary
5. Add or subtract to isolate the variable and finally
6. Use the multiplication or division or reciprocal properties to solve for the variable.

Algebra 1a: Chapter 3, Lesson 11, page 158.

More Expressions and Equations

Remember, the sum of an integer and the next integer can be represented by `x` and `(x+1)` or `x+(x+1)` or `2x+1`.

For three consecutive integers, we have `x + (x+1) + (x+2)` and if we combine like terms, it looks like `3x+3`

The sum of consecutive (comes right after each other) odd OR even integers can be expressed as `x` and `(x+2)` or `x+(x+2)` or `2x +2`.

For three consecutive ODD OR EVEN integers, we have `x + (x+2) + (x+4)` and if we combine like terms, it looks like `3x+6`

If you get confused, just make a little table, like `3`, `4`, `5`, `6`, `7` and `8` and see where the variable `n ` would line up if the numbers were hidden.

Here is a link that shows a few examples too.

Two of tonight’s homework problems solved by MrE are here! Just click it!

Algebra 1a: Chapter 3, Lesson 10, page 152.

Using Percent
The ratio of numbers to 100 is called percent. Percent means “per one hundred”. We use whickity-whack divide, the method that Ms. Phillips taught us in 7th grade. Here is my podcast that describes the process!

Two of tonight’s homework problems solved by MrE are here! Just click it!

Algebra 1a: Chapter 3, Lesson 9, page 148.

Proportions

A ratio of 2 quantities is a comparison, often expressed as a fraction. An equation that states that 2 ratios are equal is called a proportion. I prefer to just criss-cross, or cross multiply proportional problems, but the book’s way is OK too.

For example,

`x/63=2/9`, I solve by criss-crossing. That becomes

`x*9=2*63` or `9x=63*2` or `9x=126`

and dividing both sides by 9 to clear the x, gives us `x=14`.

Here is a link from purplemath.com that has some more examples.

Two of tonight’s homework problems solved by MrE are here! Just click it!