Today:

Warm-Up: Khan Academy Topics Review Fraction/Percent

Conversions Absolute Value Equations

Class Work

October 20, 2014

Warm Up Section

of Your

Notebook, please

A riparian buffer is an area around a stream that’s covered in vegetation. It protects the water in the stream from activity happening near its location.

A farm is located near a riparian buffer. The buffer begins S feet from the edge of the farm and ends B feet from the farm. How wide is the riparian buffer?

SB

BS

8 12

12 8

= + .2

= +

= = 1.45 kilometers

Cross Multiply? Y or N

Create a visual of some type

𝟏𝟕𝟏𝟐𝟎

= 8 = 8.8 meters

Class Notes

Section of Your

Notebook, please

How to easily order fractions using cross-multiplication

42

45 5/6 is > 7/9

Order from least to greatest:

Instead of finding a common denominator for 6 and 9,

In this case, however...Be aware and flexible, take the path of least resistance.

State whether the first fraction is <, >, or = to the second.

Changing Fractions to DecimalsThere are three methods to changing fractions to

decimals. The method used is determined by the denominator of the fraction. 1. If the denominator is a place value: 10, 100, 1000, etc. The decimal will match the place value of the denominator.

Changing Fractions to Decimals

2. If the denominator is a factor of a place value (can be divided evenly by 10, 100, 1000, etc.), multiply by the number needed for the product to equal the closest place value.

3. If the denominator is not a factor of a place value, then the numerator is divided by the denominator.

Solve

= 7x

Solving Absolute Value Equations

When solving an equation, isolate the absolute value expression first.

Rewrite the equation as two separate equations.

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

Once the absolute value is isolated, the grouping symbols can be taken off.

= 7x =x -7

The solutions are:

Solving Absolute Value Equations

What are the solutions to the equation

To solve (after the absolute value is isolated), split into two equations:• One with a positive 6• The other with the opposite of six,

-6• Then solve each individually

|

𝟑 𝒙=𝟔 𝟑 𝒙=−𝟔

x = 2; x = -2

What is the solution for this equation?

= 3x6 or–=x

= 6x3 or–=x

= 4x6 or–=x

= 4x3 or–=x

=32x – 9

Always check your solutions.

Rewrite the absolute value equation as two equations.=32x – 9 Rewrite as two equations.=32x – 9–or

Solve each equation separately.

Solve 72x + 5 = 4–3

First, rewrite the equation in the form

bax+ = c

Solving Absolute Value Equations

Write original equation.72x + 5 = 4–3

Add 5 to each side.72x + = 93

Divide each side by 3.72x + = 3

=72x + 3 =72x + 3–or

Next, rewrite as two equations, then solve each one.

X = -2, or x = -5

Decide if an equation has any solutions

Solve 53x + 6 =+ 2

Write original equation.53x + 6 =+ 2

Subtract 6 from each side.53x + = 4–

The absolute value of a number is never negative. So, there are no solutions.

9t + 5 = - 3–4

Decide if an equation has any solutions

Are there any solutions?

What’s the next step?

That decision cannot be made until the absolute value is

isolated.

Class Work: Absolute Value Expressions &

Equations

An absolute value equation can have two, one, or even no solutions.

Solve the equation.

5m 4 =+ 2–2

2n 7 =3– + – 10–

An NFL football must be inflated to an air pressure of 13 psi with an absolute error of 0.5 psi. Find the minimum and maximum acceptable air pressures for an NFL football.

ANSWER no solution

ANSWER 12.5 psi, 13.5 psi

ANSWER 1,– 3–

ANSWER 7.4, 7.4–

ANSWER 16, 2–5.

Solve the equation.

=7r – 9

s 4.1 = 18.92 +6.

ANSWER 15–3,–