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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
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


Ex 2 graph the solution
Ex 2: values of the variable that make at least one of the inequalities true.Graph the solution.

A) 2x – 1 < 3x and x > 4x – 9.


1 4 solving inequalities

B) 3x + 9 < -3 or -2x + 1 < 5 values of the variable that make at least one of the inequalities true..


1 4 solving inequalities

  • Classwork/Homework: values of the variable that make at least one of the inequalities true.

  • Page 24 #3-11, 17-28


Essential question
Essential values of the variable that make at least one of the inequalities true.Question:

What are the similarities and differences between inequalities and equations?

Answer on your paper in complete sentences.