Download U1L8 Solving and Graphing Inequalities

Unit 1: Relationships between Quantities and Reasoning with Equations
Lesson 8- Solving and Graphing Inequalities
Objectives:
 I can compare numbers using =, >, or <.
 I can use the properties of real numbers and inequality to
solve inequalities.
 I can graph the solution to an inequality on a number line.
 I can solve and graph compound inequalities.
Warm Up: Compare using =, >, or <.
5 ____ 2
-3 _____ -5
-3 ______ -1
¾ ______ 0.75
0.25 ______ 0.2
1/3 _____ 0.3
Properties of Inequality:
The properties of real number apply to expressions in both equations
and inequalities, and the properties of equality have corresponding
properties of inequality.
For example, according to the addition property of inequality, if a>b,
then a+c > b+c. This means that inequalities can be solved by using
many of the same steps you would use to solve equations.
Recall the steps to solve an equation…
We can follow these same steps to solve inequalities. Except when
we are multiplying or dividing by a NEGATIVE NUMBER.
Don’t forget…
When you multiply or divide by a negative number, you must
reverse the inequality sign.
Let’s try to solve a few…
4x + 5 > -3
-2x + 5 < 7
3(2x – 1) + 2 > 7x + 3
3x + 2x – 6 < 5x + 4
Now you try!
2x – 5 < 11
-2(x -1) > -12
Graphing Inequalities:
Think about what the solution to an inequality really represents. Is
there one answer that would make the statement true? Is there more
than one answer that would make the statement true?
We can represent the answer to an inequality on a number line. We
can shade the parts of the number line that satisfy the inequality.
Let’s try a few…
Graph the solution.
x > -2
4>x
x<3
-3 < x
Now it’s your turn!
Solve the inequality and graph the solution.
2x – 5x + 1 < 10
3x + 4 > 5x – 6
Compound Inequalities:
In some cases, you will need more than one inequality or a
compound inequality to describe a situation. For example, a realworld situation may be represented by x > -3 and x < 2. Some
compound inequalities, such as the one just described, can also be
written in the form -3 < x < 2.
Let’s try to graph this inequality…
You try!
Graph.
x < 0 or x > 5
4<x<6
x > -1 and x < 3
Solving Compound Inequalities:
To solve a compound inequality we will use the same properties as
we did earlier, except we will apply the property to each part of the
inequality.
Let’s try a few…
5 < 2x – 1 < 9
-12 < -3(x + 2) < 0
3x + 4 > 16 or -2x > 10
================================
Solve and graph your solution.
-4x + 5 < 2x – 2x + 7
18 < 2x + 4 < 22
Name: _________________________
Unit 1 Lesson 8: Solving and Graphing Inequalities
Solve and graph.
1) 3x – 1 < 11
2) -2(3x + 4) > 19
3) ½ x – 2 < 4
4) -2x + 4 > 5x + 7
5) 3(x – 1) + 5 < -4x + 8 + 4x
6) 3x > 15 or x + 5 < 5
7) -4x + 3 < -5 or 2x + 1 < 7
8) -3 < 2x + 1 < 5
9) 9 > -4x – 3 > -7
10) Write a compound “and” inequality that has no solution. Justify
your answer by graphing the solution on a number line.