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(25.1 hrs)Khan Academy Info.

Equation PracticeIncluding Absolute Value

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Class Notes:

Absolute Value Equations

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

|3 𝑥|=6To solve (when the absolute value is by itself), split into two equations:• One with a positive 6• The other with a

negative 6

Then solve each individually

3 𝑥=6 3 𝑥=−6

Check for UnderstandingWhat 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? There are 2 differences. 1st: The original equation is always a positive. For example, |3x + 1| = 52nd: Given |3x + 1| = 5, the second equation is really written as:

- |3x + 1| = 5; The opposite of the absolute value.... So, the opposite of -|3x - 1| = 5; Therefore, Our shortcut is to put the negative on the other side, because it works out the same. If the original absolute value equation equals a negative number, there is no solution.

-3x = 6; -3x/-3 = 6/-3; x = 2

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

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

a. 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

For the Negative Value:1. Goal: Isolate the absolute value a. Subtract 1 b. Divide by 3 c. Then Change sign to negative d. add 1; x = -2

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. Change the sign on the right only after isolating the

absolute value.4. Solve each equation individually

5.Check your answers by plugging them in!

Warm-Up

Emergency Khan Academy Questions:

Combining Like Terms with Distribution

Warm-Up

1. Write and solve an equation with distribution.

2. Write and solve an equation with distribution and a variable on each side. The answer must be a whole number.

3. |x/5| = 2

3. |x/5| = 2; |x/5| = - 2

Equations: Build from the ground up

Absolute Value

4. 3|x + 6| + 12 = 18Solve for the positive first

c. Subtract 6 from each side d. x = ?

Warm-Up

Goal: Get the absolute value by itself on the left side.a. Subtract 12 from each side b. divide by 3

Solve for the opposite next

Goal: Get the absolute value by itself on the left side before changing the sign on the right side.a. Subtract 12 from each side b. divide by 3c. We have |x + 6| = 2; Now we can change the

equation to: x + 6 = -2

-4

d. Solving, we get x = 2. The solution is x = - 4, or x = - 8

Class Work: Handout: Please use separate page for NUMBERED scratch paper.