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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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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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