Solving Inequalities

Solving Inequalities

Essential Question:

How do I solve linear inequalities?

Learning Target:

I can use the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.

On the next slide, you will complete the warm-up. Read the question carefully. You do not need to solve and will type your response.

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You will have 5 minutes to work on the warm-up

​Warm-up

Open Ended

Let's review your responses

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​Discussion

Reminder:

Open circle - does not contain solution

Closed circle - contains solution

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Express the solution set in words, in set notation, and graphically on the number line.

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Example 1

You will work on the next

​5 problems in pairs. You will either show your work and graph, provide a verbal response, or a written response.

You will have 3 minutes per problem.

​Collaborative Pairs

Draw

Find the solution set to

$$x\ +\ 4\ \le\ 7$$

Express in set notation and on the number line

Open Ended

Find the solution set to

$$\frac{m}{3}\ +\ 8\ \ne\ 9$$

Explain how you found the solution and where it is graphed on the number line

Draw

Find the solution set to

$$8y\ +\ 4\ <\ 7y\ -\ 2$$

Express the solution in set notation and on a number line.

Audio Response

Find the solution to the

$$6\left(x\ -\ 5\right)\ \ge\ 30$$

Explain how you found the solution and where to graph on the number line.

Open Audio Recorder

Draw

Find the solution

$$4\left(x\ -\ 3\right)\ >\ 2\left(x\ -\ 2\right)$$

Express the solution in set notation and on the number line.

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​How did your partner contribute to solving and graphing each inequality?

Class Discussion

What happens to the inequality symbol when you divide or multiply by a negative value?

Example 2

You will work with your partners again to solve 3 more inequality problems out of the 4 seen shown here.

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​You will be given three minutes for each problem.

Collaborative Pairs

Draw

Find the solution

$$6\ -\ a\ \ge\ 15$$

Express the solution in set notation and on the number line.

Draw

Find the solution to

$$-3\left(2x\ +\ 4\ \right)\ >\ 0$$

Express the solution in set notation and on the number line.

Draw

Find the solution to

$$-\frac{x}{12}\le\frac{1}{4}$$

Express the solution in set notation and on the number line.

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​How did your partner contribute to solving and graphing each inequality?

Class Discussion

Multiple Choice

Solve the inequality

-5x - 7 < -28

• x > -7

• x < -7

• $$x\ >\ \frac{21}{5}$$

• $$x\ <\ -\frac{21}{5}$$

Multiple Choice

Solve the inequality.

2(b - 8 ) > 12

• b > 20

• b > 6

• b > 14

• b < 20

Goal Met!

I can use the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.

Application

Application