Lesson #14- Solving Inequalities

Intervals

ba

[a,b]

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{x ∈ R | a ≤ x ≤ b}

Inequalities are the _______ of equalities.

5x = 2x + 9

Equality

opposite

Inequality

2y = 35 +7y a2 = b2 + c2

3y < 10

8y – 5 > 2710a + 5b ≥ 27

For inequalities we use <, ≤, ≥, or > symbols.

eg. 1 x + 30 > 40

x > 10

-30 -30 This says that x can beany value greater than 10.

€

{x ∈ R | x >10}]10,+∞[+∞10

# Line Interval Set Builder

eg. 2 5x + 12 ≤ 3x+ 20

5x ≤ 3x +8

-12 -12

-3x -3x 2x ≤ 82 2

x ≤ 4

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{x ∈ R | x ≤ 4}] -∞,4]

This says, x is any value less than or equal to 4.

4-∞

# Line Interval Set Builder

eg. 3 -5x ≤ 2x- 21 -2x -2x

-7x ≤ -21-7 -7 x ≥ 3

€

{x ∈ R | x ≥ 3}[ 3, ∞[+∞3

Math Gods

“When you divide by a negative

switch the direction of the inequality

symbol.”

# Line Interval Set Builder

eg. 4 2(x-1) - 3(x+1) ≤ 0 2x

≤ 0 +5 +5 -x ≤ 5

-1 -1

€

{x ∈ R | x ≥ −5}[-5, +∞[

-2 - 3x - 3 ≤ 0-x -5

x ≥ -5

+∞-5

# Line Interval Set Builder

Homework

pg. 81-82 #3pg. 84 #6,7a-d & 8