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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.

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

- 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 4 7? NO!
- But 7 4 7 4.
- The equation is still
- true if we add 4
- to both sides.

Lets try another example!

- Always check your solution!!
- The original problem is x - 6 10.
- Using the solution x16,
- Does 16 - 6 10?
- YES! 10 10 and our solution is correct.

- x - 6 10
- Add 6 to each side.
- x - 6 10
- 6 6
- x 16

What if we see y (-4) 9?

- Check your solution!
- Does 13 - 4 9?
- YES! 99 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

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)-105?
- 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...

The answers...

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