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# 1-4 Solving Inequalities - PowerPoint PPT Presentation

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

Big Idea:

-Solve equations and 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!

3x ≥ 15

Multiplying

Ex 1: solve and Graph each solution.

A) -2x < 3(x – 5)

B) 7x > 7(2 + x)

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

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.

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.

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

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

• Page 24 #3-11, 17-28

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?