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algebra

Algebra

Solutions of Equations and Inequalities

By: Mr. Schwark

solve for a variable
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
Equation Form
  • 2X + 4 = 10
  • X – 3 = 7
  • 5X – 10 = 20 – 5X
solve for x
Solve for X
  • Get X by itself

- Get X on only one side

  • X = ?
how to get x alone
How to Get X Alone

- Use Basic Math to Solve

  • (−) Subtract
  • (+) Add
  • (x) Multiply
  • (÷) Divide
basic rules
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
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
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
Solve for Inequalities
  • What is an Inequalities
    • < Less then
    • > Greater then
    • < Less then or equal to
    • > Greater then or equal to
examples of inequalities
Examples of Inequalities
  • X + 3 < 5
  • 2X – 6 > 8
  • 4X + 2 < 10
  • -6X – 10 > 20
solve for inequality
Solve for Inequality
  • Solve same as Equation
  • Get X by itself
  • X = ?
rules of inequalities
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
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
Graph an Inequality
  • < = ) Less then
  • > = ( Greater then
  • < = ] Less then or equal
  • >= [ Grater then or equal
examples of graph
Examples of Graph

X < -1

X > -2

X < 0

X > 1

citations
Citations
  • All Graphs

Schwark, Adam. Sept. 27 2011, creative commons

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