Solving Inequalities

Solving Inequalities

Key Vocabulary/Standards

• Inequality

• Combine

• Like Terms

• Opposite Operations

• Coefficient

• NC.M1.A-REI.3: Solve linear equations and inequalities in one variable. 

Multiple Choice

What is the inequality sign for greater than?

• $<$

• $>$

• $\le$

• $\ge$

Solving Inequalities

When solving inequalities the steps are the same as solving a regular equation, only difference is if you divide or multiply by a negative number the inequality sign flips directions.

Multiple Choice

If you divide an inequality with a less than sign by -3, what inequality sign would it change to?

• $>$

• $<$

• $\ge$

• $\le$

Solving Inequality Steps

• Get rid of all Parentheses

• Combine like terms

• Move all x terms to the left hand side (LHS)

• Move all constants to the right hand side (RHS)

• Get rid of the x’s coefficient by doing the opposite operations (multiplication -> division or division -> multiplication)

• BE CAREFUL WHEN DIVIDING/MULTIPLYING BY A NEGATIVE

Example 1

- 8x + 2x - 16 < - 5x + 7x

(-8x + 2x) - 16 < (-5x + 7x)

-6x - 16 < 2x

-6x - 16 - 2x < 2x - 2x

-8x - 16 < 0

-8x - 16 + 16 < 0 + 16

-8x < 16

-8x/-8 < 16/-8

x > -2

Multiple Choice

When looking at this inequality what should be your first step? $-1-6x-6>-11-7x$  

• Get rid of parentheses

• move x terms to the LHS

• combine like terms

• move the constant to the RHS

Example 2

- 1 - 6x - 6 > - 11 - 7x

(-1 - 6) - 6x > -11 - 7x

-7 - 6x > -11 - 7x

-7 - 6x + 7x > -11 - 7x + 7x

-7 + x > -11

-7 + x + 7 > -11 + 7

x > -4

Multiple Choice

You try!

Solve.
 $1-3x\ +6x>10-6x$  

• x > 1

• x < -1

• x > 9

• x < 9

Multiple Choice

When looking at this inequality what should be your first step? $3(1-2x)>3-6x$  

• Get rid of parentheses

• move x terms to the LHS

• combine like terms

• move the constant to the RHS

Poll

How comfortable are you with solving inequalities?

• Great!

• So-so

• Totally Confused