Bell Ringer

Darius saw a shirt that was on sale for 20% off. The original price of the shirt was $28. If tax was 9%, how much did Darius pay for the shirt?

Discount: $28 • .20 = $5.60 off Sale Price of Shirt: $28 – $5.60 = $22.40 Tax: $22.40 • .09 = $2.016 (Tax) Final Cost: $22.40 + $2.016 = $24.416

$24.42

Homework

1. x = 22. x = 53. x = 74. x = 45. x = 06. x = 37. x = 98. x = 4/3 or 1 1/3 or 1.33

Selected Problems

#3 -5x – 6 = -7x + 8 + 6 + 6 -5x = -7x + 14 +7x +7x 2x = 14 x = 7

#5 2(x + 3) = -2x + 6 2x + 6 = -2x + 6 – 6 – 6 2x = -2x +2x +2x 4x = 0 x = 0

Selected Problems

#7 2(2x – 1) = 3x + 7 4x – 2 = 3x + 7 + 2 + 2 4x = 3x + 9 -3x -3x x = 9

#8 x + 5 = -2x + 9 – 5 – 5 x = -2x + 4 +2x +2x 3x = 4 x = 4/3 or 1 1/3 or 1.33

Manipulating and Solving Equations

XEI 601: Manipulate expressions and equations

Manipulating Equations

Like we saw last Friday, we often have to simplify equations before we solve them.

We have to distribute, combine like terms, and move terms before solving.

We will continue to work on those skills today.

Combining Like Terms

7x + 8 = 5x + 12 – 8 – 8

7x = 5x + 4 – 5x – 5x

2x = 4 x = 2

Move all of the variables to

the left.

Move all of the numbers to the right.

Solve for X

Combining Like Terms

4x – 7 + 2x = -2x + 17 + 7 + 7

4x + 2x = -2x + 24

6x = -2x + 24 + 2x +2x 8x = 24 x = 3

Distributive Property

3(2x – 4) = 2x 6x – 12 = 2x + 12 +

12 6x = 2x + 12 – 2x – 2x 4x = 12 x = 3

Distribute

Move

Solve

Distributive Property

-4(2x – 5) = -2(3x + 1) -8x + 20 = -6x – 2

– 20 – 20 -8x = -6x –

22 +6x +6x

-2x = -22 x = 11

What is wrong with me?

-3(x – 2) = -2x + 4 -3x – 6 = -2x + 4

+ 6 + 6 -3x = –2x

+ 10 +2x +2x

-x = 10 x = 10

What is wrong with me?

-5x – 5 + 2x = -2x + 5 +

5 -5x + 2x = -2x

+ 5 -3x = -2x + 5

-5x = 5 x = 1