Unit 3: Equations and Inequalities

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Click here to go to the IXL website for all kinds of 8th grade topics and review problems.

Equations

What is an equation?

Examples: 4 + 3  = 7        or        3x + 5 = 10

An equation is a number sentence. We call it an equation because it has an equal sign.

The 5 Steps to Writing an Equation or Inequality

Step 1. Read and underline the question

Step 2. Find your  Χ  (your variable/unknown) and BOX it

Step 3. Circle the Math Words (product, quotient, each,                per, together, sum, difference, squared)

Step 4. Replace the operation words with their symbols (              • , + , – ,  ÷ , / , = , < , > , ≤ , ≥ ,√ , ≠ , ² , ³ )

Step 5. Write the equations

 Don’t forget our cool ‘dance’ we did to remember this!

WRITING EQUATIONS PRACTICE PROBLEMS:

Click here to practice Writing Equations online and get automatic feedback (it grades it)! 🙂

With Equations, Inequalities and Expressions we always want to combine like terms 1st!

Here is an example on how to do that:

3.4 Combining Like Terms

Once all like terms have been combined then we can solve.

Solving Equations with Models

To create your own equations using models click here!

MODELING EQUATIONS PRACTICE PROBLEMS:

Click here to practice Modeling Equations online and get automatic feedback (it grades it)! 🙂

Solving Equations Algebraically

Here is another example solving algebraically

Solve √(x/2) = 3

Start With √(x/2) = 3
Square both sides: x/2 = 32
32 = 9: x/2 = 9
Multiply both sides by 2: x = 18

And the more “tricks” and techniques you learn the better you will get.

Here is an example of how we solved equations in class:

3.9 Solving Equations with variables on both sides

SOLVING EQUATIONS (with variables on both sides PRACTICE PROBLEMS:

Click here or here to practice Solving Equations online and get automatic feedback (it grades it)! 🙂

Systems of Equations

For information on systems of equations click here.

Simple vs. Compound  Interest

Introduction to interest:

http://www.mathsisfun.com/money/interest.html

SIMPLE INTEREST

 I = Prt  

  • I = interest owed  [$] (this is ONLY the interest borrowed)
  • P = amount borrowed (called “Principal”)  [$]
  • r = interest rate   [%] (you have to divide the percent by 100)  For information On Percents click here!
  • t = time    [years]

Simple interest is money you can earn by investing some money (the principal). The interest (percent) is the rate that makes the money grow!

COMPOUND INTEREST

 A = P(1+r)^t  

  • A = All of it / Actual / total amount owed (this amount includes the interest and the principal)   [$]
  • P = amount borrowed (called “Principal”)    [$]
  • r = interest rate     [%]
  • t = time    [years]

Compound interest is very similar to simple interest. The difference is that compound interest grows much faster! The reason it grows faster is because the interest (percent) has an exponent.

********** MAKE SURE TO READ THE QUESTION AND SEE EXACTLY WHAT IT IS ASKING DOES IT JUST WANT THE INTEREST OR THE TOTAL (All of it) ???????? *************************

For information on compound interest click here.

SIMPLE INTEREST PRACTICE PROBLEMS:

Click here or here to practice Simple Interest online and get automatic feedback (it grades it)! 🙂

COMPOUND INTEREST PRACTICE PROBLEMS:

Click here or here to practice Compound Interest online and get automatic feedback (it grades it)! 🙂

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