Math 7 ( Period 4)

Solving Equations Using All for Ops 2.5 and 2.6

What’s the GOAL?  Determine the value of the variable?

How?  Isolate the variable—get it alone on one side of the equation

What do I do? Use inverse (opposite operations to “get rid” of everything on the side with the variable

What should my focus be?  When equations get really complicated…. ALWAYS focus on the variable FIRST!

One Step Equations with all 4 Operations

 –We will be meeting 4 new BFF’s

Equation Balancing Properties of Equality – there are 4 of them

Whatever YOU DO to BALANCE an equation – that operation is the property of equality that was used.

If you have…

X + 3 = 10  …you used the subtraction property  of Equality because you need to SUBTRACT 3 from both sides equally.

x – 3 = 10 …you used the Addition Property of Equality because you need to ADD 3 to each side equally

3x = 9 … you used the Division Property of Equality because you need to DIVIDE  each side by 3 equally

x/3 = 9…  you used the Multiplication Property of Equality because you need to MULTIPLY both sides by 3 equally.

TWO more Properties

Additive Inverse
using the opposite sign of the term given in the equation results in the term dropping out because it simplifies to 0

Multiplicative Inverse
using the reciprocal of the term given in the equation results in the term dropping out because it simplifies to 1

Here are the steps and justifications

1. Focus on the side where the variable is and focus specifically on what is in the way of the variable being by itself (isolated)

2. What is the operation that the variable is doing with that number in its way?

3. Get rid of that number by using the opposite (inverse) operation

Golden Rule of Equations:

Whatever you do to one side do unto the other side

Doing the same thing on both sides is actually the new set of properties (your new BFF’s)

When you multiply equally, it’s the multiplication property of equality

When you divide equally, it’s the division property of equality

When you add equally, it’s the addition property of equality

When you subtract equally, it’s the subtraction property of equality

4. JUSTIFICATION  You have just used one of the properties of equality… Which one?

Whatever operation you used to balance both sides (not the operation of the original equation)

5.You should now have the variable all alone (isolated) on one side of the equal sign.

6. JUSTIFICATION?  Why is the variable alone?  For + and -, you used the Identify Property of Addition ( ID+) which simply means that you don’t bring down the ZERO because when you add ZERO it does not change anything! ( NOTE:  There is no ID of subtraction)

For ×   and  ÷  you used the Identity Property of Multiplication ( ID x) which simply means that you don’t bring down the ONE because when you multiply by one it doesn’t change anything ( NOTE: There is no ID of division!)

FORMAL CHECK:

There are three steps to a formal check:

1. Rewrite the original equation FROM THE ORIGIANL SOUSE – this is just o case that ou find out you copied the problem wrong

2. Substitute your answer where the variable is and QUESTIO you answer by placing a “?” over the equal sign

3. REALLY  Do the math and finally set both sides equal. Place a check mark, a happy face… to indicate that you really did check this!