Do Now 3/5/14 Take out HW from last night. Take out HW from last night. –Text p. 463, #2-36 evens...
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Do Now 3/5/14 Do Now 3/5/14 Take out HW from last night. Take out HW from last night. – Text p. 463, #2-36 evens Text p. 463, #2-36 evens Copy HW in your planner. Copy HW in your planner. – Practice worksheet 11.4 B Practice worksheet 11.4 B In your notebook, answer the following In your notebook, answer the following question. Outside of the math classroom, question. Outside of the math classroom, where have you heard phrases such as “at where have you heard phrases such as “at least” or “no more than”? Give examples. least” or “no more than”? Give examples. How would you write the phrases How would you write the phrases mathematically? mathematically?
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Transcript of Do Now 3/5/14 Take out HW from last night. Take out HW from last night. –Text p. 463, #2-36 evens...
Do Now 3/5/14Do Now 3/5/14 Take out HW from last night.Take out HW from last night.
– Text p. 463, #2-36 evensText p. 463, #2-36 evens
Copy HW in your planner.Copy HW in your planner.– Practice worksheet 11.4 BPractice worksheet 11.4 B
In your notebook, answer the following question. In your notebook, answer the following question. Outside of the math classroom, where have you Outside of the math classroom, where have you heard phrases such as “at least” or “no more heard phrases such as “at least” or “no more than”? Give examples. How would you write the than”? Give examples. How would you write the phrases mathematically?phrases mathematically?
HomeworkHomework Text p. 463, #2-36 evens Text p. 463, #2-36 evens
2) isolate the variable2) isolate the variable 4) proportion4) proportion 6) -816) -81 8) 128) 12 10) 7/6 or 1 1/610) 7/6 or 1 1/6 12) 7/9912) 7/99 14) -914) -9 16) 816) 8 18) 2518) 25
20) -4720) -47 22) 522) 5 24) -0.7524) -0.75 26) 2626) 26 28) 1/828) 1/8 30) 4.530) 4.5 32) 87.532) 87.5 34) 534) 5 36) 4536) 45
ObjectiveObjective
SWBAT read and write SWBAT read and write inequalities and graph them on a inequalities and graph them on a number linenumber line
Section 11.4, “Inequalities”Section 11.4, “Inequalities”
INEQUALITIESINEQUALITIES – – mathematical sentence formed mathematical sentence formed by placing a <, ≤, >, or ≥ by placing a <, ≤, >, or ≥ between two expressions. between two expressions.
y – 8 < 12 y – 8 < 12
13 13 ≥≥ 14 - z14 - z
11 + a 11 + a ≤≤ 121121
x +8 > 30
x +8 > 30
Writing InequalitiesWriting Inequalities
SymbolSymbol MeaningMeaning Key PhraseKey Phrase
Is less thanIs less than Fewer than, Fewer than, belowbelow
Is less or equal toIs less or equal to At most, no At most, no more thanmore than
Is greater thanIs greater than More than, More than, aboveabove
Is greater than Is greater than or equal toor equal to
At least, no At least, no less thanless than
<<
≤ ≤
>>
On a number line, the On a number line, the GRAPH OF GRAPH OF AN INEQUALITYAN INEQUALITY is the set of points is the set of points that represent the that represent the SOLUTION SETSOLUTION SET of the inequality.of the inequality.
x < 8x < 8
55 66 77 88
x ≥ 11x ≥ 11
1212 13131111 14141010
““Less than” and “greaterLess than” and “greaterthan” are representedthan” are representedwith an open circle.with an open circle.
““Less than or equal to” Less than or equal to” and “greater than or equaland “greater than or equalto” are represented with a to” are represented with a closed circle.closed circle.
101099 1111
88 99
Graph each inequalityGraph each inequality
x < -3x < -3
-6-6 -5-5 -4-4 -3-3
x ≥ 7x ≥ 7
88 9977 101066
““Less than” and “greaterLess than” and “greaterthan” are representedthan” are representedwith an open circle.with an open circle.
““Less than or equal to” Less than or equal to” and “greater than or equaland “greater than or equalto” are represented with a to” are represented with a closed circle.closed circle.
-1-1-2-2 00
44 55
Graph each inequalityGraph each inequality
7 ≥ y7 ≥ y
88 9977 101066
““Less than or equal to” Less than or equal to” and “greater than or equaland “greater than or equalto” are represented with a to” are represented with a closed circle.closed circle.
44 55
-1 < h-1 < h
-4-4 -3-3 -2-2 -1-1
““Less than” and “greaterLess than” and “greaterthan” are representedthan” are representedwith an open circle.with an open circle.
1100 22
SOLUTIONSOLUTION
Write an inequality represented by the graph.Write an inequality represented by the graph.
The closed circle means that The closed circle means that 88 is not a solution of is not a solution of the inequalitythe inequality.. Because the arrow points to the Because the arrow points to the leftleft,, all numbers less than all numbers less than 88 are solutions are solutions..
ANSWERANSWER
An inequality represented by the graph is An inequality represented by the graph is x x << 88..
SOLUTIONSOLUTION
The closed circle means that The closed circle means that –– 2.5 2.5 is a solution of is a solution of the inequalitythe inequality.. Because the arrow points to the Because the arrow points to the rightright,, all numbers greater than all numbers greater than –– 2.5 2.5 are solutionsare solutions..
ANSWERANSWER
An inequality represented by the graph is An inequality represented by the graph is x x > > –– 2.5. 2.5.
Write an inequality represented by the graph.Write an inequality represented by the graph.
SOLUTION
The highest temperature recorded in the United States The highest temperature recorded in the United States was was 134°F134°F at Death Valley, California, in at Death Valley, California, in 19131913. Use only . Use only this fact to write and graph an inequality that this fact to write and graph an inequality that describes the temperatures in the United States.describes the temperatures in the United States.
Let T represent a temperature (in degrees Fahrenheit) in the United States. The value of T must be less than or equal to 134. So, an inequality is T ≤ 134.
COMPOUND INEQUALITYCOMPOUND INEQUALITY – – consists of two separate consists of two separate inequalities joined by inequalities joined by ANDAND or or OROR..
““AND” AND” Compound InequalitiesCompound Inequalities
The graph of a compound inequality with The graph of a compound inequality with ANDAND is the is the INTERSECTIONINTERSECTION of the graphs of the inequalities. of the graphs of the inequalities.
Graph x > -2Graph x > -2
00 11-1-1 22-2-2 33
Graph x ≤ 1Graph x ≤ 1
00 11-1-1 22-2-2 33
Graph of x ≤ 1 and x > Graph of x ≤ 1 and x > -2-2
00 11-1-1 22-2-2 33
Graph -2< x ≤ 1 Graph -2< x ≤ 1
““OR” OR” Compound InequalitiesCompound Inequalities
The graph of a compound inequality with The graph of a compound inequality with OROR is is the the UNION UNION of the graphs of the inequalities.of the graphs of the inequalities.
Graph x > 2Graph x > 2
00 11-1-1 22-2-2 33
Graph x ≤ -1Graph x ≤ -1
00 11-1-1 22-2-2 33
Graph of x ≤ -1 or x > Graph of x ≤ -1 or x > 22
00 11-1-1 22-2-2 33
Graph each compound Graph each compound inequalityinequality
5 < y ≤ 95 < y ≤ 9
88 9977 10106644 55
h > 1 or h ≤ -3 h > 1 or h ≤ -3
-4-4 -3-3 -2-2 -1-1 1100 22
Graph each compound Graph each compound inequalityinequality
y ≤ 16 or y > 20y ≤ 16 or y > 20
1818 19191717 202016161414 1515
h > -3 and h ≤ 0 h > -3 and h ≤ 0
-4-4 -3-3 -2-2 -1-1 1100 22
Translate the verbal phrase into an inequality. Translate the verbal phrase into an inequality. Then Then
graph the inequality.graph the inequality.All real numbers that are greater than All real numbers that are greater than –– 22 and and lesslessthan than 3.3.
InequalityInequality::
Graph:Graph:
All real numbers that are less than All real numbers that are less than 00 or or greater thangreater thanor equal to or equal to 2.2.
Inequality:Inequality:
Graph:Graph:
– – 2 < 2 < x x < 3< 3
x x < 0 < 0 or x or x ≥ 2≥ 2
Challenge
HomeworkHomeworkPractice worksheets 11.4 B & CPractice worksheets 11.4 B & C
