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