Day 2: Solving One-Variable Inequalities

Warm-Up

Graph the inequality y < -3 and express in interval notation.

Solving Inequalities Using Addition and Subtraction

Solving inequalities with addition and subtraction is just like solving equations.

ExerciseFind the solution set of each inequality. Graph and express in interval notation and set builder notation

1) Set-builder Notation:
Interval Notation:

2) Set-builder Notation:
Interval Notation:

Solving Inequalities with Multiplication and Division

As you saw, solving inequalities using addition and subtraction is just like solving equations. However, when it comes to multiplication and division, there is one slight difference.

This difference involves multiplication and division by negative numbers.

Consider this example. What inequality sign belongs in the box?

______

When multiplying or dividing both sides of an inequality by a negative number, the sense of the inequality changes.

The “sense” of the inequality refers to the statement that the inequality is making.

Note: We do not change the sense of the inequality when we reverse the entire statement. We simply change its direction.

For example:

4 > 3 and 3 < 4 / These inequalities are the same.
We did not change the sense of the inequality.
4 > x and x < 4 / These inequalities are the same.
We did not change the sense of the inequality.
x < 4 and x > 4 / These inequalities are different.
One says that x is greater than 4 and one says it is less.
We DID change the sense of the inequality.

Model ProblemsSolve and graph each inequality. Write the solution in set-builder and interval notation.

1)

Set-builder Notation:

Interval Notation:

2)

Set-builder Notation:

Interval Notation:

3)

Set-builder Notation:

Interval Notation:

4) Set-builder Notation:

Interval Notation:

ExerciseSolve and graph each inequality. Write the solution in set-builder and interval notation.

1) Set-builder Notation:

Interval Notation:

2) Set-builder Notation:

Interval Notation:

3) Set-builder Notation:

Interval Notation:

4) Set-builder Notation:

Interval Notation:

ChallengeExpress each phrase using an inequality.

x is a positive number ______x is not a negative number ______

x is a negative number ______

Homework

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