Download Multi-Step Inequalities

Algebra I
6.1 – 6.3 Graphing & Solving Inequalities
Name ______________________
Date _______________ Block __
GRAPHING INEQUALITIES
The graph of an inequality with one variable is the set of points that represent all
solutions of the inequality.
To graph the solution to an inequality with one variable:
 Use an open circle
for < or >
 Use a closed circle
for ≤ or ≥
 Remember to label your number line (label UNDER the number line)
Examples
Graph of x < 3
Graph of x ≥ -1
Your Turn
Graph the following inequalities.
1.
x>4
2.
y ≤ -2
3.
p <5
4.
m ≥ -3
SOLVING INEQUALITIES WITH ONE VARIABLE
Solving inequalities is much like solving equations.
The goals are still the same:
 Get the variable on one side.
 Get the constants on the other side.
The BIG DIFFERENCE is …
When you multiply or divide by a negative,
FLIP the inequality symbol!
To check solutions:
 If your inequality symbol is < or >, use the solution
o if your answer is x > -3, use -3 since -3 is in the set of answers
 If your inequality symbol is < or >, use a number that makes the statement true
o if your answer is x > 3, pick a number greater than 3 (like 4!)
o if your answer is x < 3, pick a number smaller than 3 (like 2!)
 If your answer is a fraction, use the next integer to check
Examples: Solve each inequality. Check your answer. Then, graph your solution.
1.
x–3<2
2.
-3x > 12
3.

x
 30
5
Multi-Step Inequalities
We use the same steps to solve multi-step inequalities as we did to solve multi-step
equations (just remember: with inequalities, when you multiply or divide by a negative, flip
the inequality symbol).
Steps to solving inequalities:
 Isolate the variable on the LEFT side of the inequality.
 Add or subtract to isolate the variable term.
 Multiply or divide to isolate the variable.
 Remember to FLIP the symbol when you multiply or divide by a negative!
Try These:
1.
3x – 7 < 8
4.
6x  3  3x  2
2.
-3(w + 12) < 0
3.
5.
2x  14  4x  4
6.
4 – 2m > 7 – 3m
8  23x  4  10x  20
SPECIAL CASES
As with equations, inequalities can also have special cases.
Inequalities can have the following answers:
 No solutions – the inequality is false (just like no solutions for equations)
 All real numbers – the inequality is true (similar to identity for equations)
Solve the inequality, if possible.
a.
14x + 5 < 7(2x – 3)
b.
12x – 1 > 6(2x – 1)