confidential1 our lesson. confidential2 warm up 1)18n – 3 = 6 1/2 2)5 = 15b + 2 1/5 3)27.8 + 7.5v...
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Confidential 1
Our Lesson
Confidential 2
Warm up
1)18n – 3 = 6 1/2
2)5 = 15b + 2 1/5
3)27.8 + 7.5v = 32.75 0.66
4)2.5 (w+ 2) = 14 3.6
5)30k -12 = 28 + 10k 2
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1.Combine like terms
2. Isolate the variable you wish to solve for
3.Substitute your answer into the original equation and check that it works
Steps for Solving Two step Equations
Lets recap what we have learnt in the last lesson
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Step 1: Combine Like Terms
Combine together the terms containing the variable
Like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient.
Step 1
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When the variable does not have a coefficient of one, we will need to isolate the variable itself
When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable
Step 2
Step 2: Isolate the variable itself
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Substitute Your Answer into the Original Equation
Substitution is a process of replacing variables with numbers or expressions
By substituting, we switch or exchange values, often replacing a variable with a numerical value
We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation
Step 3
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Lets get Started
Words or phrases often suggest addition, subtraction, multiplication and division
In this lesson we will see how to translate verbal phrases in to algebraic expressions
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Shaina is three years older than her sisterShaina is three years older than her sister
The number is twice as much The number is twice as much
The weight is 5 less than half of it The weight is 5 less than half of it
Examples
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Addition Subtraction
Words used to express Addition/Subtraction
PlusSumMore than Increased by Total
MinusDifferenceLess thanLessDecreased by
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Words used to express Multiplication/Division
Multiplication Division
TimesProductMultipliedOf TwiceThrice
DividedQuotient
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USING A VERBAL MODEL
In Mathematics there is a difference between a phrase and a sentence. Phrases translate into
expressions; sentences translate into equations or inequalities
Expressions
Phrases
Equations or Inequalities
Sentences
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PHRASE TO EXPRESSION
Phrase Expression
The sum of six and a number
6 + x
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Sentence Equation
The sum of six and a number is twelve.
6 + x = 12
In this sentence, “is” says that one quantity is equal to one another.
SENTENCE TO EQUATION
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Sentence Inequality
The sum of six and a number is less than twelve.
6 + x < 12
In this sentence, the words “is less than” indicate an inequality.
SENTENCE TO INEQUALITY
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USING A VERBAL MODELUSING A VERBAL MODEL
Phrase Expression
=
Sentence Equation
Sentence Inequality
The sum of six and a number is twelve.
6 + x = 12
In this sentence, “is” says thatone quantity is equal to one another
In this sentence, the words “is less than” indicate an inequality
The sum of six and a number is less than twelve.
6 + x < 12 is less than twelve.
6 + x < 12
The sum of six and a number 6 + x
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TRANSLATING VERBAL PHRASES
Seven divided by a number
The sum of six and a number 6 + x
Eight more than a number
A number plus five
A number increased by seven
A number decreased by nine
Ten times a number
y + 8
10 • n or
n
n + 5
x + 7
n – 9
(10n)
7x
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1)Three runs less than the pirates scored y – 3
2)Twice as many tomatoes as last year 2a
3)Five more than a number is 25 5 + m = 25
4)Six fewer hours than her sister s -6
5)Half the population of Texas p/2
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6) Seven times the cost is $63 7c = 63
7) He weighs 180 pounds, which is 22 pounds 180 = 2z-22less than double her weight
8) 4 times as many bees 4b
9) Five more hits than the Martins h + 5
10) Three more than 8 times as many trees is 75 trees 8t – 3 = 75
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Break Time
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6/1/6 Review of Integers
GAME
Click here to play a Game
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1)You and three friends are having a dim sum lunch at a Chinese restaurant that charges $2 per plate. You order lots of plates. The waiter gives you a bill for $25.20, which includes tax of $1.20. Use mental math to solve the equation for how many plates your group ordered.
Your group ordered 12 plates of food costing $24.00.
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2) JET PILOT A jet pilot is flying from Los Angeles, CA to Chicago, at a speed of 500 miles per hour. When the plane is 600 miles from Chicago, an air traffic controller tells the pilot that it will be 2 hours before the plane can get clearance to land. The pilot knows the speed of the jet must be greater then 322 miles per hour or the jet could stall. At what speed would the jet have to fly to arrive in Chicago in 2 hours?
To arrive in 2 hours, the pilot would have to slow the jet down to 300 miles per hour.As the pilot cannot travel slower than 322 miles per hour so pilot would take some other action, such as circling in a holding pattern, to use some of the time.
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3) Shopping networks on television are a popular way to shop. In addition to the cost of the items, you usually pay a shipping fee. Ramya wanted to order several pairs of running shorts that cost $12 each. The total shipping fee is $7. How many shorts can she order with $55?
12s + 7 = 5512s + 7 – 7 = 55 – 712s = 4812s = 4812 = 12 s = 4 running shorts
Subtract 7 from each side
Divide each side by 12
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Addition Subtraction
Words used to express Addition/Subtraction
PlusSumMore than Increased by Total
MinusDifferenceLess thanLessDecreased by
Lets review what we have learned in this lesson
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Words used to express Multiplication/Division
Multiplication Division
TimesProductMultipliedOf TwiceThrice
DividedQuotient
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USING A VERBAL MODEL
In Mathematics there is a difference between a phrase and a sentence. Phrases translate into
expressions; sentences translate into equations or inequalities
Expressions
Phrases
Equations or Inequalities
Sentences
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TRANSLATING VERBAL PHRASES
Eleven divided by a number
The sum of five and a number 5 + x
Twelve more than a number
A number minus nine
A number increased by four
A number decreased by nine
Six times a number
m + 12
6 • n or
n
n -9
x + 4
n – 9
(6n)
11x
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You had a Great lesson today
Be sure to practice what you have learned
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