6th Grade Math Textbook, Fundamentals

Lesson 3-4 for exercise sets. &KDSWHU 

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Solve and graph each inequality. Check your work to justify your answer.

1.n  814 2. 4 n  9 3.d(3)  2

4.Discuss and Write How is solving inequalities involving addition and

subtraction like solving addition and subtraction algebraic equations?

Solve:  22 x  6 Graph:

 22  6 x 6  6

 16 x Simplify.

The solution set is all numbers that are less

than 16.

Check: According to the solution set,

17 is a solution and 16 is not.

 22  17  6 Substitute 17 for n.  22  16  6 Substitute 16 for n.

 22  23 Tr u e  22  22 False

So the circle on the number line is correct. So the direction of the ray is correct.

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Add 6 to both sides

to isolate x.

1

After you solve an inequality, you can use a number line to graph

and check the solution set.

Solve:s 4 15

s 4  415  4

s 11 Simplify.

The solution set is all numbers that are greater than or equal to 11.

Graph:

Subtract 4 from both sides to isolate s.

Since s 11, use a dot and a ray extending toward the right to indicate that

numbers greater than or equal to 11 are in the solution set.

5 6 7 8 9 10 11 12 13 14 15

Think

Integers, fractions, and decimals greater

than or equal to 11 are solutions.

Check: According to the solution set, both 11 and 13 are solutions.

11 4 15 Substitute 11 for s. 13 4 15 Substitute 13 for s.

15 15 Tr u e. 17 15 Tr u e

So the dot on the number line is correct. So the direction of the ray is correct.

??

Think

Integers, fractions, and decimals less than 16 are solutions.

Since  16 x, use a circle and a ray

extending toward the left to indicate that

numbers less than 16, not including 16,

are in the solution set.

 20  19  18  17  16  15  14  13  12