Friday, September 27, 2013

Today:Make-Up Tests Now

Warm-UpAbsolute Value Equations

Khan Academy Due Sunday: 7:00 pmClass work:

Warm-Up (5); fr. Test

Version 1

3) 5(4d – 2) = 2d -1 A) 2 B) C) 4 D) 9 E) None4) 7x – 5 – x = -1 – 6x + 6 – 3x A) B) 1 C) 3 D) 1 E) 1

1) .3x + .3 = .6x + .7 - .5x A) .32 B) 15 C) 2 D) .4 E) None

8) - 6 = x - (2 + x) A) 28 B) -18 C) 30 D) -22 E) 32

Version 2

Version 39) The first stage of a rocket burns 28 seconds longer than

the second stage. If the total burning time for both stages is 182 seconds, how many seconds does the first stage burn for?

A) 124 B) 77 C) 98 D) 90 E) 105

Absolute ValueThe distance away from 0

0 5-5 10-10

10 10𝑥=−10 𝑥=10

Absolute ValueWhat two points are 5 away

from 0?

0 5-5 10-10

Solving Absolute Value Equations

What are the solutions to the equation

To solve (when the absolute value is by itself), split into two equations:• One with a positive 3x• The other with the

opposite of 3x = 6Then solve each individually

3 𝑥=6 −3 𝑥=6

|

What are x = 2; x = -2

Because the |x|could be positive or negative, (why)we must solve for both possibilities.

Check for Understanding

What is the solution to |3x + 1| = - 5

There is no solution. The result of an absolute equation can never be negative.

But what about the second equation that we write using a negative sign? The difference is: The original equation is always a positive. For

example, |3x + 1| = 5

If the original absolute value equation equals a negative number, there is no

solution.

Guided PracticeEx.1: 3|x - 1| + 1 = 10

For the Positive Value:1. Goal: Isolate the absolute

valuea. Subtract 1b. Divide by 3

c. add 1. x = 4

3|x - 1| + 1 = 10 - 1 - 1

3|x - 1| = 9 |x - 1| = 3

x = 4

3|x - 1| + 1 = 10 - 1 - 1

3|x - 1| = 9 -x + 1 = 3

-x = 2; x = -2

For the Negative Value:1. Goal: Take the

opposite of the absolute value

2. a. Subtract 1 b. Divide by 3 c. Take the opposite of the ab. value d. add 1; x = -2 Plug in and check each value!!!!

SummaryWhat are the steps to solve an absolute value

equation?

1. Is the Absolute Value alone (isolated) on one side?

2. Split the Absolute Value into two equations3. One equation takes the absolute value, one

takes the opposite of the absolute value4. Solve each equation individually5. Check your answers by plugging them in!

3. || = 2 3. = 2; - = 2; x = ?, and ?

Absolute Value

4. |x + 6| + 12 = 18

Solve for the positive first

b. Subtract 6 from each side. x = ?

Goal: Get the absolute value by itself on the left side.

a. Subtract 12 from each side

0

Warm-Up

Solve for the negative next

Goal: Get the absolute value by itself on the left side before taking the opposite:

a. Subtract 12 from each side

b. We have |x + 6|= 6; Now we can change the equation to: -|x + 6|, or -x - 6 = 6; -x = 12; x = -12 The solutions are x = 0, or x = -12

Absolute Value

e. Plug in each value. Are both -4 & -8 solutions?

Absolute Value: Last Problem

The highest elevation in North America is Mt. McKinley, which is

20,320 feet above sea level. The lowest

elevation is Death Valley, which is 282 feet below sea level. What is the

distance from the top of Mt. McKinley to the

bottom of Death Valley?

Class Work: Handout: Please use separate page for

NUMBERED scratch paper.