1. Solving Equations Using Addition and Subtraction
Objectives:
A.4f Apply these skills to solve practical problems.
A.4b Justify steps used in solving equations.
Use a graphing calculator to check your solutions.

2. To Solve an Equation means...
To isolate the variable having a coefficient of 1 on one side of the equation.
Ex: x = 5 is solved for x.
y = 2x - 1 is solved for y.

3. Addition Property of Equality
For any numbers a, b, and c, if a = b, then a + c = b + c.
What it means:
You can add any number to BOTH sides of an equation and the equation will still hold true.

4. An easy example: We all know that 7 = 7. Does 7 + 4 = 7? NO!
Would you ever leave the house with only one shoe on?
Would you ever put blush on just one cheek?
Would you ever shave just one side of your face?
We all know that 7 = 7.
Does = 7? NO!
But =
The equation is still
true if we add 4
to both sides.

5. Let’s try another example!
Always check your solution!!
The original problem is x - 6 = 10.
Using the solution x=16,
Does = 10?
YES! 10 = 10 and our solution is correct.
x - 6 = 10
Add 6 to each side.
x = 16

6. What if we see y + (-4) = 9? Check your solution!
Does = 9?
YES! 9=9 and our solution is correct.
Recall that y + (-4) = 9
is the same as y - 4 = 9.
Now we can use the addition property.
y - 4 = 9
+4 +4
y = 13

7. How about z = 7?
Remember to always use the sign in front of the number.
Because 16 is negative, we need to add 16 to both sides.
-16 + z = 7
z = 23
Check you solution!
Does = 7?
YES! 7 = 7 and our solution is correct.

8. A trick question... Check your solution! Does -(-15)-10=5?
-n = 15
Do we want -n? NO, we want positive n.
If the opposite of n is positive 15, then n must be negative 15.
Solution: n = -15
Check your solution!
Does -(-15)-10=5?
Remember, two negatives = a positive
= 5 so our solution is correct.

9. Subtraction Property of Equality
For any numbers a, b, and c, if a = b, then a - c = b - c.
What it means:
You can subtract any number from BOTH sides of an equation and the equation will still hold true.

10. 3 Examples: 1) x + 3 = 17 3) z - (-5) = -13 -3 -3
x = 14
Does = 17?
2) 13 + y = 20
y = 7
Does = 20?
3) z - (-5) = -13
Change this equation. z + 5 = -13
z = -18
Does -18 -(-5) = -13?
= -13
-13 = -13 YES!

11. Try these on your own...

12. The answers...