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# math - PowerPoint PPT Presentation

Math

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## PowerPoint Slideshow about 'math' - schwa2aj

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Presentation Transcript

### Algebra

Solutions of Equations and Inequalities

By: Mr. Schwark

Solve for a Variable
• A variable represents a number
• We do not know the number
• X will be the variable
• We will solve for X
Equation Form
• 2X + 4 = 10
• X – 3 = 7
• 5X – 10 = 20 – 5X
Solve for X
• Get X by itself

- Get X on only one side

• X = ?
How to Get X Alone

- Use Basic Math to Solve

• (−) Subtract
• (x) Multiply
• (÷) Divide
Basic Rules
• Get X by itself
• Note: If you preform an operation to one side, you also must preform the same operation to the other side.
Lets Try Examples
• Ex 1

3X + 5 = 20

-5 -5

3X = 15

÷3 ÷3

X = 5

• Ex 2

1/2X – 10 = 0

+10 +10

1/2X = 10

x2 x2

X = 20

- Plug in your value for X -

• Ex 1

3(5) + 5 = 20

15 + 5 = 20

20 = 20

• Ex 2

½(20) – 10 = 0

10 – 10 = 0

0 = 0

Solve for Inequalities
• What is an Inequalities
• < Less then
• > Greater then
• < Less then or equal to
• > Greater then or equal to
Examples of Inequalities
• X + 3 < 5
• 2X – 6 > 8
• 4X + 2 < 10
• -6X – 10 > 20
Solve for Inequality
• Solve same as Equation
• Get X by itself
• X = ?
Rules of Inequalities
• Same rules as equations
• With one exception:
• When dividing by a negative you must switch the direction of the sign.
Lets Try Examples
• Ex 1

-2X – 10 < 4

+10 +10

-2X < 14

÷(-2) ÷(-2)

X > -7

• Ex 2

3X + 15 > 9

-15 -15

3X > -6

÷3 ÷3

X > -2

Graph an Inequality
• < = ) Less then
• > = ( Greater then
• < = ] Less then or equal
• >= [ Grater then or equal
Examples of Graph

X < -1

X > -2

X < 0

X > 1

Citations
• All Graphs

Schwark, Adam. Sept. 27 2011, creative commons