inequalities
DESCRIPTION
solve & graph inequalitiesTRANSCRIPT
Agenda Monday, Nov. 23
Homework 8 p. 136 # 12 - 20
p. 142 # 10 - 14, 39, 77, 79
p. 149 # 13 - 20, 29, 30
Don't panic, we will have some time in Flex to get started.
Daily Scribe? Monday _____________ Tuesday ____________
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Chapter Three - Inequalities: graphs & solutions
ADVISORYYou must be at least 35 inches tall in order to ridePirate Lagoon.
Express this statement using algebra
Let x represent the height.
x ≥ 35The Management
36" 35" 34"
Which of the triplets can ride?
x ≥ 35
Which graph represents the inequality x ≥ 35
x > 35
x < 35
x ≤ 35
Match the inequality to the graph
x ≥ 35
x ≥ 35
x ≤ 35
x > 35
x < 35
x < 45
x ≥ 25
x ≤ -5
x > -2
Graph these inequalities on the number line
x < 45
x ≥ 25
x ≤ -5
x > -2
Solution
2x + 1 ≤ 5
x + 5 > 11
Identify the values which make the inequality true
}{{7,8,9,10}
{-5,-4,-3,-2,-1,0,1,2}
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-5 -4 -3 -2 -1 0 1 2 3 4 5
}{
3x - 4 > 14
x + 4 ≤ 3
Solve these inequalities
5Solve as inequality thesame way you would solve a linear equation.Instead of "=" you have">, <, ≥ or ≤".
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
3x - 4 + 4 > 14 + 43x > 183x >1833x > 6
-5 -4< TRUE
When you multiply or divide an inequality by a negative number the direction of the inequality must be reversed.
Multiply both sides by -1
>
5 4> TRUE
FALSE
Multiplying or dividing by a negative number
-5 -4
3 - > 8
x24x + 2 >
10
- 4x + 2 > 10
3 + > 8
x2
Solve these inequalities
x > 2 x < 2
x < -10 x > -10
x > 2
x < -2x > -2
x < 10 x > 10
x > 10
3 - - 3 > 8 - 3
x2
x2 - >
5x2
(-2) < (5)(-2)
-
x < -10
- 4x + 2 - 2 > 10 - 2 - 4x > 8
8 4-
x -4-4 <
x < -2
4x + 2 > 10
3 - > 8
x2
- 4x + 2 > 10
3 + > 8
x2
The value the circle lies on is included in the solution set.
Closed circle
Open circle
The value the circle lies on is not included in the solution set.
Open or closed?
back to page 3
Triangle Inequality:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
draw and measure the lengths of three trianglessmall medium large sm +
med
Compare the sum of the measures of the small and medium sides to the measure of the largeside for each triangle you created. Describe what you notice.
Triangle Inequality:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
draw and measure three lengths that cannot make a triangle
small medium large sm + med
Compare the sum of the measures of the small and medium sides to the measure of the largeside for each non-triangle you created. Describe what you notice.
Compare the sum of the measures of the small and medium sides to the measure of the largeside for each triangle you created. Describe what you notice.
Compare the sum of the measures of the small and medium sides to the measure of the largeside for each non-triangle you created. Describe what you notice.Make a conjecture. Based on your observations, write a conjecture about the relationshipbetween the sum of the measures of the small and medium sides of a triangle and the measure ofthe large side of the triangle. Provide a reason for your conjecture.
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