Algebra
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Algebra l.jpg

Algebra

Solutions of Equations and Inequalities

By: Mr. Schwark


Solve for a variable l.jpg
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 l.jpg
Equation Form

  • 2X + 4 = 10

  • X – 3 = 7

  • 5X – 10 = 20 – 5X


Solve for x l.jpg
Solve for X

  • Get X by itself

    - Get X on only one side

  • X = ?


How to get x alone l.jpg
How to Get X Alone

- Use Basic Math to Solve

  • (−) Subtract

  • (+) Add

  • (x) Multiply

  • (÷) Divide


Basic rules l.jpg
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 l.jpg
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


Check the answers l.jpg
Check the Answers

- 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 l.jpg
Solve for Inequalities

  • What is an Inequalities

    • < Less then

    • > Greater then

    • < Less then or equal to

    • > Greater then or equal to


Examples of inequalities l.jpg
Examples of Inequalities

  • X + 3 < 5

  • 2X – 6 > 8

  • 4X + 2 < 10

  • -6X – 10 > 20


Solve for inequality l.jpg
Solve for Inequality

  • Solve same as Equation

  • Get X by itself

  • X = ?


Rules of inequalities l.jpg
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 examples13 l.jpg
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 l.jpg
Graph an Inequality

  • < = ) Less then

  • > = ( Greater then

  • < = ] Less then or equal

  • >= [ Grater then or equal


Examples of graph l.jpg
Examples of Graph

X < -1

X > -2

X < 0

X > 1


Citations l.jpg
Citations

  • All Graphs

    Schwark, Adam. Sept. 27 2011, creative commons


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