1. Do Now
Solve the equations for the variable. -6(-p + 8) = -6p (-7 – x) = 36 + (1 + 7x)

2. Solving Equations Match-up

3. Solving Inequalities
Lesson 1-5

4. What is an inequality?
An inequality is whenever two expressions are NOT equal.
Inequalities use special symbols to represent the relationship between the two quantities.
less than ( < ), greater than ( > )
less than or equal to ( ≤ ), greater than or equal to ( ≥ )
not equal to ( ≠ ).

5. When do we use inequalities?
We use them whenever a scenario has a constraint or limit.
To get a raise at her job, Kayla needs to sell at least 50 magazine subscriptions this month.
Carlos can take at most 10 friends on his trip to Europe.

6. Solving Inequalities
We solve inequalities the same way that we solve equations EXCEPT:
In an inequality, if you multiply or divide both sides by a negative number, you must flip the inequality.

7. Solving Equations vs. Solving Inequalities
c + 13 = r = 70
c + 13 ≥ r < 70

8. Examples
p – 9 ≤ k ≥ n + 5 < 𝑥 3 >6

9. Exit Ticket
Solve the equation for the variable. 5(n – 7) = 2(n + 14) Solve the inequalities. -11x > -99 x + 9 ≤ 15

10. Do Now
Graph the inequalities on a number line. x < 3 -3 ≥ x 9 > x x ≤ −1

11. Solving Inequalities in One Variable
Lesson 1-5

12. Graphing Inequalities
To graph an inequality,
Draw a number line with labels at integer values.
Graph an open dot at the solution value.
Leave the dot open if the inequality is > or <.
Color in the dot if the inequality is ≥ or ≤.
Pick a value that makes the inequality true and shade that side of the number line.

13. Examples
Solve the inequalities and graph the solution. -12 > x – 7 a – 17 ≥ 16 𝑦 −3 <8

14. Solving Inequalities
The steps to solve inequalities are just like the ones we use to solve equations.
The only differences are:
When you divide or multiply both sides by a negative number, then you flip the inequality symbol.
We always graph the solution on a number line.

15. Solving Equations vs Solving Inequalities
Solving an equation
Solving an inequality
3x – 5 = – 6x = 76
3x – 5 < – 6x ≥ 76

16. Examples
Solve the inequalities and graph the solution. 2x + 4 ≥ 8 𝑚 3 −3≤−6 -4(-4 + x) > 56

17. With a Partner…
Solve the inequalities and graph the solutions. -3(2x + 2) < 10 2(4 – 2x) > 1

18. On your Own
Solve the inequalities and graph the solution. -b – 2 > 8 -3(r – 4) ≥ 0 4+ 𝑛 3 <6

19. Example
Solve -4(3x – 1) + 6x ≥ 16 and graph the solution.

20. Independent Practice p. 34 12, 13, 16 – 22 even, 29 - 34

21. Do Now
Solve the inequalities and graph the solution. −5(2x + 1) < x + 6 ≤ 2.4x 4(3 − 1 2 𝑥) ≥ −4

22. Homework Questions?

23. Solving Inequalities with a Variable on Both Sides
Lesson 1-5

24. Examples
Solve the inequalities and graph the solution. 3.5x + 19 ≥ 1.5x – 7 -3(2x – 5) > -6x + 9

25. Example
Solve the inequality 4x – 5 < 2(2x – 3) and graph the solution.

26. Solution Types
If an inequality solution has an answer that is a false inequality, then there is no solution.
EX: -3 < -9
EX: 0 ≥ 5
If an inequality has an answer that is a true inequality, then there are infinitely many solutions.
EX: 14 > 10
EX: -7 ≤ -7

27. Examples
Solve each inequality. -2(4x – 2) < -8x x – 5 < -3(2x + 1)

28. On your Own
Solve the inequalities. −5n – 6n ≤ 8 – 8n – n −2(5 + 6n) < 6(8 – 2n)

29. Word Problem
Door #1
Door #2

30. Word Problem #1
Deandre makes $10 an hour working at Best Buy. He wants to buy a new iPhone X which costs $999. Write an inequality to represent how long Deandre will have to work to be able to buy the iPhone.

31. Word Problem #2
Ashanti can spend up to $8 on her lunch. She wants to buy a tuna sandwich, a bottle of apple juice, and x pounds of potato salad. Write and solve an inequality to find the possible number of pounds of potato salad she can buy.
Menu Item
Cost
Tuna Sandwich
$4.25
Potato Salad
$4.00/lb
Apple Juice
$2.25

32. Exit Slip
Solve the inequalities. 3x – 24 ≤ -2(2x – 30) 2x + 12 > 2(x + 6)