Solving Equations Using Addition and Subtraction

• 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.

Objectives:

Must have the word doc. To complete the class notes as you review this PPT

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.

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.

An easy example:

We all know that 7 = 7.

Does 7 + 4 = 7? NO!

But 7 + 4 = 7 + 4.

The equation is still

true if we add 4

to both sides.

• 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?

Let’s try another example!x - 6 = 10

Add 6 to each side.

x - 6 = 10 +6 +6 x = 16

• Always check your solution!!

• The original problem is x - 6 = 10.

• Using the solution x=16,Does 16 - 6 = 10?

• YES! 10 = 10 and our solution is correct.

What if we see y + (-4) = 9?

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

• Check your solution!

• Does 13 - 4 = 9?

• YES! 9=9 and our solution is correct.

How about -16 + 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

+16 +16

z = 23

• Check you solution!

• Does -16 + 23 = 7?

• YES! 7 = 7 and our solution is correct.

A trick question...-n - 10 = 5

+10 +10

-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

• 15 - 10 = 5 so our solution is correct.

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.

3 Examples:1) x + 3 = 17

-3 -3

x = 14• Does 14 + 3 = 17?

2) 13 + y = 20

-13 -13

y = 7• Does 13 + 7 = 20?

3) z - (-5) = -13

• Change this equation. z + 5 = -13

-5 -5

z = -18

• Does -18 -(-5) = -13?

• -18 + 5 = -13• -13 = -13 YES!

Try these on your own...

x + 4 = -10 x – 14 = -5

y – (-9) = 4 3 – y = 7

12 + z = 15 -5 + z = -7

The answers...

x = -14 x = 9

y = -5 y = -4

z = 3 z = -2