Algebra Solutions of Equations and Inequalities By: Mr. Schwark
AlgebraSolutions 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
•(+) Add
•(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 13X + 5 = 20 -5 -5 3X = 15 ÷3 ÷3 X = 5
•Ex 21/2X – 10 = 0
+10 +10
1/2X = 10
x2 x2
X = 20
Check the Answers
•Ex 1 3(5) + 5 = 20 15 + 5 = 20
20 = 20
•Ex 2½(20) – 10 = 0 10 – 10 = 0 0 = 0
- Plug in your value for X -
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 23X + 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 < 0
X > -2
X < -1
X > 1
Citations
•All GraphsSchwark, Adam. Sept.
27 2011, creative commons