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1-4 Solving Inequalities. Big Idea: -Solve equations and inequalities. Solving and Graphing Inequalities. As with an equation, the solutions of an inequality are the numbers that make it true. The properties for solving inequalities are similar to the properties for solving equations.

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1-4 Solving Inequalities

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1 4 solving inequalities

1-4 Solving Inequalities

Big Idea:

-Solve equations and inequalities.


Solving and graphing inequalities

Solving and Graphing Inequalities

As with an equation, the solutions of an inequality are the numbers that make it true.

The properties for solving inequalities are similar to the properties for solving equations.

The exception occurs when you multiply or divide each side by a negative.

MULTIPLYING OR DIVIDING BOTH SIDES BY A NEGATIVE REVERSES THE INEQUALITY SYMBOL!


1 4 solving inequalities

Dividing

3x ≥ 15

Multiplying


Ex 1 solve and graph each solution

Ex 1: solve and Graph each solution.

A) -2x < 3(x – 5)


1 4 solving inequalities

B) 7x > 7(2 + x)


Compound inequalities

Compound Inequalities

Compound Inequality: a pair of inequalities joined by “and” or “or”.

Ex: -1 < x and x ≤ 3 same as -1 <x ≤ 3

x < 2 or x ≥ 5


1 4 solving inequalities

To solve a compound inequality containing “and”, find all values of the variable that make both inequalities true.

-Name a student that is a girl and wearing red

-Name a teacher that is female and is short

-Find x such that x > 2 and x ≤ 5.


1 4 solving inequalities

  • To solve a compound inequality containing “or”, find all values of the variable that make at least one of the inequalities true.

    -Name a sport that involves water or a puck.

    -Name a teacher that is male or teaches Lang. Arts.

    -Find x such that x < 0 or x ≥ 5.


Ex 2 graph the solution

Ex 2: Graph the solution.

A)2x – 1 < 3x and x > 4x – 9.


1 4 solving inequalities

B) 3x + 9 < -3 or -2x + 1 < 5.


1 4 solving inequalities

  • Classwork/Homework:

  • Page 24 #3-11, 17-28


Essential question

Essential Question:

What are the similarities and differences between inequalities and equations?

Answer on your paper in complete sentences.


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