linear inequality

1. LINEAR
INEQUALITY IN
ONE VARIABLE
ax + b < c

2. SITUATION

3. SITUATION
A student should spend no
more than 2 hours a day on
social media. Let t represent
the time (in hours) spent
online.

4. SITUATION
A student should spend no
more than 2 hours a day on
social media. Let t represent
the time (in hours) spent
online.
How can we represent this as a
mathematical sentence?

5. SITUATION
A student should spend no
more than 2 hours a day on
social media. Let t represent
the time (in hours) spent
online.
How can we represent this as a
mathematical sentence?
t 2
≤

6. Symbol Meaning Example Read as
INEQUALTY
SYMBOL

7. Symbol Meaning Example Read as
<
INEQUALTY
SYMBOL

8. Symbol Meaning Example Read as
< less than
INEQUALTY
SYMBOL

9. Symbol Meaning Example Read as
< less than x < 4
INEQUALTY
SYMBOL

10. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
INEQUALTY
SYMBOL

11. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
>
INEQUALTY
SYMBOL

12. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than
INEQUALTY
SYMBOL

13. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2
INEQUALTY
SYMBOL

14. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
INEQUALTY
SYMBOL

15. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤
INEQUALTY
SYMBOL

16. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to
INEQUALTY
SYMBOL

17. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to a 10
≤
INEQUALTY
SYMBOL

18. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to a 10
≤ a is at most 10
INEQUALTY
SYMBOL

19. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to a 10
≤ a is at most 10
≥
INEQUALTY
SYMBOL

20. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to a 10
≤ a is at most 10
≥
greater than or equal to
INEQUALTY
SYMBOL

21. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to a 10
≤ a is at most 10
≥
greater than or equal to
b -3
≥
INEQUALTY
SYMBOL

22. Symbol Meaning Example Read as
< less than x < 4 x is less than 4
> greater than y > 2 y is greater than 2
≤ less than or equal to a 10
≤ a is at most 10
≥
greater than or equal to
b -3
≥ b is at least -3
INEQUALTY
SYMBOL

23. LINEAR
INEQUALITY IN
ONE VARIABLE
ax + b < c

24. LINEAR INEQUALITY

25. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:

26. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c

27. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c
ax + b > c

28. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c

29. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥

30. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥
where a, b, and c are real number, a ≠ 0

31. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥
where a, b, and c are real number, a ≠ 0
Examples:

32. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥
where a, b, and c are real number, a ≠ 0
Examples:
2x + 3 < 7

33. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥
where a, b, and c are real number, a ≠ 0
Examples:
2x + 3 < 7
5x – 2 > 8

34. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥
where a, b, and c are real number, a ≠ 0
Examples:
2x + 3 < 7 3x 9
≤
5x – 2 > 8

35. LINEAR INEQUALITY
A linear inequality is a mathematical
statement that relates a linear expression as
either less than or greater than the other. It
can be written in the form:
ax + b < c ax + b c
≤
ax + b > c ax + b c
≥
where a, b, and c are real number, a ≠ 0
Examples:
2x + 3 < 7 3x 9
≤
5x – 2 > 8 -2(4x – 5) < 9 – 2(x – 2)

36. SOLVING LINEAR INEQUALITY IN ONE VARIABLE

37. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

38. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
Steps:
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

39. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
Steps:
1.Simplify both sides
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

40. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
Steps:
1.Simplify both sides
2.Isolate the variable
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

41. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
Steps:
1.Simplify both sides
2.Isolate the variable
3.When you multiply or divide both side by a negative number,
reverse the inequality sign
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

42. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
Steps:
1.Simplify both sides
2.Isolate the variable
3.When you multiply or divide both side by a negative number,
reverse the inequality sign
4.Write the solution set
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

43. A solution to a linear inequality is a number
that makes the inequality a true statement
when substituted for the variable. Linear
inequalities can have infinitely many
solutions or no solution at all.
Steps:
1.Simplify both sides
2.Isolate the variable
3.When you multiply or divide both side by a negative number,
reverse the inequality sign
4.Write the solution set
5.Graph the solution on a number line
SOLVING LINEAR INEQUALITY IN ONE VARIABLE

44. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE

45. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE Inequalities can be graphed on the number line as
rays. If the inequality is “strict” (< or >), we use an
open dot to indicate that the endpoint of the ray is
not part of the solution. For the other types of
inequalities ( and ), we use a closed dot.
≤ ≥

46. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE Inequalities can be graphed on the number line as
rays. If the inequality is “strict” (< or >), we use an
open dot to indicate that the endpoint of the ray is
not part of the solution. For the other types of
inequalities ( and ), we use a closed dot.
≤ ≥
EXAMPLES:

47. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE Inequalities can be graphed on the number line as
rays. If the inequality is “strict” (< or >), we use an
open dot to indicate that the endpoint of the ray is
not part of the solution. For the other types of
inequalities ( and ), we use a closed dot.
≤ ≥
x > 3
EXAMPLES:

48. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE Inequalities can be graphed on the number line as
rays. If the inequality is “strict” (< or >), we use an
open dot to indicate that the endpoint of the ray is
not part of the solution. For the other types of
inequalities ( and ), we use a closed dot.
≤ ≥
x > 3
EXAMPLES:
< l l l l l l l l l >
0 1 2 3 4 5 6 7 8

49. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE Inequalities can be graphed on the number line as
rays. If the inequality is “strict” (< or >), we use an
open dot to indicate that the endpoint of the ray is
not part of the solution. For the other types of
inequalities ( and ), we use a closed dot.
≤ ≥
x > 3
EXAMPLES:
< l l l l l l l l l >
0 1 2 3 4 5 6 7 8
x 3
≤

50. GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE Inequalities can be graphed on the number line as
rays. If the inequality is “strict” (< or >), we use an
open dot to indicate that the endpoint of the ray is
not part of the solution. For the other types of
inequalities ( and ), we use a closed dot.
≤ ≥
x > 3
EXAMPLES:
< l l l l l l l l l >
0 1 2 3 4 5 6 7 8
x 3
≤
< l l l l l l l l l >
0 1 2 3 4 5 6 7 8

51. SOLVING AND GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE

52. SOLVING AND GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE
Examples:

53. SOLVING AND GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE
Examples:
-2x + 1 21
≥

54. SOLVING AND GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE
Examples:
-2x + 1 21
≥
2x – 8 < 14

55. SOLVING AND GRAPHING LINEAR INEQUALITY IN ONE
VARIABLE
Examples:
-2x + 1 21
≥
2x – 8 < 14
4x – 4 12
≥

56. PRACTICE
Try this!
-5x + 3 < 28

57. PRACTICE
Try this!
-5x + 3 < 28
1/2x – 7 < 13