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Inequality SymbolsInequality Symbols
Less than
Greater than
Less than or equal to
Greater than or equal to
Not equal to
Name:Date:Period:
Topic: Solving Inequalities Essential Question: What is the correlation between solving equations and solving inequalities?
Warm-up: Name the following inequality signs:
An inequality is like an equation, but instead of an equal sign (=) it
has one of these signs:
Vocabulary:
Solving Inequalities
by
Adding or Subtracting
Solving the Inequality
w + 5 < 8
Note:
We will use the same steps that we did with equations, if a number is added to
the variable, we subtract the same number to both sides.
Answer
w + 5 < 8
w + 5 -5 < 8 -5
w + 0 < 3
w < 3 All numbers less than 3 are
solutions to this problem!
Now you try it!
8 + r ≥ -2
x - 2 > -2
4 + y ≤ 1
7 > x – 5
x + 2 ≤ 3
Answers to Practice Problems:8 + r ≥ -2
8 -8 + r ≥ -2 -8
r + 0 ≥ -10
w ≥ -10
All numbers from -10 and up (including
-10) make this problem true!
x - 2 > -2
x - 2 + 2 > -2 + 2
x + 0 > 0
x > 0
All numbers greater than 0 make this problem true!
4 + y ≤ 1
4 - 4 + y ≤ 1 - 4
y + 0 ≤ -3
y ≤ -3
All numbers from -3 down (including -3) make this problem
true!
Answers to Practice Problems: x - 5 > 7
x + 2 ≤ 3
x – 5 + 5 > 7 + 5
x + 0 > 12
x > 12
120
x + 2 - 2 ≤ 7 - 2
x + 0 ≤ 5
x ≤ 5
0 5
x < 5
What do these means?What do these means?
x ≤ 3
x > 4 x ≥ 2
How to graph the solutions
> Graph any number greater than. . .
open circle, line to the right
< Graph any number less than. . .
open circle, line to the left
Graph any number greater than or equal to. . .
closed circle, line to the right
Graph any number less than or equal to. . .
closed circle, line to the left
x < 5
x ≤ 3
x > 4
x ≥ 2
Solving Inequalities
by
Multiplying or Dividing
Solving the Inequality
< - 2
15b < 60
< - 2
15b < 60
Answers
x > 4
15b < 6015 15
b < 4
x < - 8
But wait there is one special case:
●Sometimes you may have to reverse the direction of the inequality sign!!
●That only happens when you multiply or divide both sides of the inequality by a negative number.
That was easy!!!
- 4r > 16
Solving the Inequality
Answers
(
((
(
m < - 10
- 4r > 16 - 4r > 16 - 4 - 4 r < - 4
Solving multi-step inequalitiesis like
solving multi-step equations.If you can solve
1132 xyou can solve
1132 x
1132 x 1132 x
Remember:
Which graph shows the solution to 2x - 10 ≥ 4?
Now you try it!Page 181 (1 – 4, 8, 16, 20)
1) 3(x + 4) - 5(x - 1) < 52) -2x + 6 ≥ 3x – 43) 3 (t + 1) – 4t ≥ - 54) 5m - 8 > 125) -5x – 9 < 26
Anytime you multiply or divide both sides of an
inequality by a negative number, you need to reverse
the sign.
Brief Review of InequalitiesBrief Review of Inequalities• Add/subtract the same number on each side of an inequality
• Multiply/divide by the same positive number on each side of an inequality
• If you multiply or divide by a negative number, you MUST flip the inequality sign!
Wrap-Up:
Home-Learning:
Page 175 (34), Page 176 (70),
Page 181 (12, 21, 24), Page 189 (2, 4),
Page 190 (20), Page 192 (59, 60)