Warm-Up (4)InequalitiesClass Work

Monday, October 21, 2032

Today:

Warm-Up Questions

1. Order of Operations: 18 - (4 + 2 * 3) + 12 18 - (10) + 12; 8 + 12 = 20

2. (6+(9−5×3))×4 =(8+(3−40))×4; =(8+

(−37))×4; =(−29)×4; = -1163. -13

10

x = - 13 Multiply each side by - 10 13x = 130; x = 10

Warm-Up Questions

4. 3|x - 3|+ 5 = - 2|x - 3| + 9 = 3|x - 3|+ 2|x - 3|= 5|x - 3|+ 5 = 9 5|x - 3|= 4; x - 3 = 4/5, -4/5x = 4/5 + 15/5; x = 19/5x = -4/5 + 15/5; x = 11/5

Introduction

to Inequalities

Understanding&

Solutions

The Prefix 'in' means not. Incorrect, Inflexible Equations which have solutions are equal to a

specific value, or number: 2x = 8 can only equal 4; no other number will satisfy this equation.

Inequalities, however, can have many answers. They are not equal to a specific value.

When solving inequalities, we are solving for a range of numbers, not just one.

Let's look at some examples of inequalities

Inequalities

InequalitiesLook at, and think about, the following

signs:

The problem is, none of these signs say what they're really supposed to say. Not only that, they are all incorrect. To be correct, they needed to include an inequality.

InequalitiesLet's put this sign in mathematical

terms:Let h = the height required to use the ride. The sign says you must be 46" tall, therefore h = 46"According to the sign, if you're not 46" tall, you cannot ride. But how many people are exactly 46" tall?

What they really meant to say was...You must be at least 46" tall, or in mathematical terms...

Your height must be equal to or greater than 46". This is our inequality. Our solution is not a single number, but a range of numbers.

InequalitiesThis sign obviously refers to the drinking age.

But the sign states that even 22 year olds, or 75 year old people cannot enter. The two words missing here are: at least

In mathematical terms, the drinking age is:

Equal to or greater than 21 d > 21

Inequalities

As far as the signs are written: Incorrect Correct

Incorrect Correct

Inequalities

Less Than; shown with an open circle on number line; x < -4

Less Than or equal to; shown with closed circle on number line; x < -4

Solving Inequalities

The process of solving Inequalities is the same as equations except for one rule(which we'll get to later), and how inequalities are shown graphically.

Solving Inequalities

Greater Than; shown with an open circle on number line; x > -4

Greater Than or equal to; shown with a closed circle on number line; x < -4

Solving Inequalities Basic Inequalities

1. Write the inequality shown below

x < 3

x > 0

-5 < x < 2

InequalitiesGraphing Inequalities

Draw a number line and graph the following:1. 1 <x < 8 2, -2 < x < -1 3. -5 < x < 2

Solving Inequalities

Solve for x and Graph

1. 6x - 7 < 5 2. 4(x - 2) > 20 3. x - 8 < - 6

1. x < 2; Graph

x > 3 x < 2

And now the one difference between equations & inequalities: Solve for x and Graph

4. -2x < 4; When multiplying or dividing by a negative coefficient, you must switch the sign

4. -2x < 4; -2x/-2 > 4/-2; x > -2

Inequalities

Think about the rule for example 4 with numbers in there, instead of variables. -2 < 4

You know that the number four is larger than the number negative two: 4 > -2.

Multiplying through this inequality by –1, we get –4 < –2, which the number line shows is true:

If we hadn't flipped the inequality, we would have ended up with "–4 > –2", which clearly isn't true.

When multiplying or dividing a negative coefficient, you must flip the sign for the inequality to remain true.

Solving Inequalities

Last 2 Practice Problems; Solve & Graph on Number Line

5. x - 12 < -6 6. 6 - 2x > - x

5. x - 12 < -6; +12 +12

5. x < 6;

6. 6 - 2x > - x +2x +2x 6 > x; x < 6

Today:

Class Work:5-1: All5-2: All

Inequalities