1. 1.3 Solving 1 Step Equations & Inequalities

2. To solve ax = b equations:
Divide both sides by a
EXAMPLE 1:
8x = 96
Divide both sides by 8 to get x by itself. x = 12

3. Try a few more… -3x = 24 -8 x = -3 -3 EXAMPLE 2:
Since x is being multiplied by -3, we need to divide by -3 to get x by itself. (Do the opposite)
-3x = 24 -8 x =

4. And another one…
EXAMPLE 3:
Try to get x by itself. So, we need to divide both sides by -2.8.
-2.8x = -9.8
x = 3.5

5. And another one…
EXAMPLE 4:
42.35 = 3.5x
x = 12.1

6. Does everyone agree: 4 > 2 Let’s discover….
What happens when we do the following…..

7. Mutliply both sides by 2…..
4 > 2
8 > 4
Is this true??
If no, what would make the inequality true?

8. 4 > 2 2 > 1 Divide both sides by 2….. Is this true??
Is this true??
If no, what would make the inequality true?

9. Multiply both sides by -2….
4 > 2
-8 > -4
Is this true??
If no, what would make the inequality true?

10. 4 > 2 -2 > -1 Divide both sides by -2….. Is this true??
Is this true??
If no, what would make the inequality true?

11. What can we conclude?
Talk with a partner about what we just discovered and form a conjecture based on our findings.

12. RULE:
When multiplying or dividing by a negative number, switch the direction of the inequality symbol:
EX: < becomes >
≥ becomes ≤
You get flipped - Rap

13. Example 5: Try this one on your own 

14. Example 6: Try this one on your own 

15. To solve ax = b if a is a fraction:
Example 7: Multiply both sides of the equation by the reciprocal of a.
Then solve like all the others! x
= -3
Multiply by the reciprocal! 9 * 9 1 1 9 9 1
x = -3 *
x = -27

16. Example 8
Multiply both sides by its reciprocal, (3/2).
X = 9

17. Another one… Example 9: -4 Multiply by the reciprocal! x = 2 3 -3 -4
4 3 -3 4
x = 2
X = -6 4

18. Example 10: Try this with your neighbor

19. Example 11 Multiply by the reciprocal!
Multiply by the reciprocal!
**Don’t forget to flip the sign!! (Since we are multiplying be a negative)

20. Example 12 Try this with a neighbor
Multiply by the reciprocal!
**Don’t forget to flip the sign!! (Since we are multiplying be a negative)

21. Are you a MASTER?
Which inequality does not have the solution x > 6?
A B C D
Example 2-6a

22. A. B. C. D.
Answer: B
Example 2-6a

23. Assignment:
Lesson 1.3
You must show work to receive credit for this assignment!