2-4 Solving Multi-Step Equations and Consecutive Integer Problems

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2-4 Solving Multi-Step Equations and Consecutive
Integer Problems
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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Solving Multi-Step Equations
The prefix multi means more than one. A
multi-step equation is solved by transforming the
equation more than one time. Always remember the
basic rule
Whatever you do to one side of the equal sign,
you must also do to the other side of the equal
sign.
When solving multi-step equations, undo the
addition or subtraction first before undoing
multiplication or division.
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Solve.
Write the problem.
Undo subtraction.
1
Undo fraction using the reciprocal.
Remember In algebra work downward. Line up the
equal signs. Skip one line after the answer.
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Solve.
Write the problem.
Undo addition.
1
Undo division.
The 5 must be in the numerator position or
midway. It should not be written in the
denominator position!
5
Solve.
Write the problem.


Change subtraction to addition and distribute.
Combine like terms.
Undo double sign.
Undo subtraction.
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Undo multiplication.
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Solve.
Example 2
Example 3
Example 1




Combine like terms.
Distribute
Are your equal signs in a line?
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Solve.
Example 4
Example 5
Example 6
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4
1
1
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Multiply both sides by the reciprocal.
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The study of numbers and the relationship between
them is called number theory.
Consecutive integers are integers in counting
order, such as 7, 8, and 9.
Beginning with an odd integer and counting by two
will result in consecutive odd integers, such as
-3, -1, 1, 3, 5
Beginning with an even integer and counting by
two will result in consecutive even integers,
such as -4, -2, 0, 2, 4
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Two consecutive integers have a sum of 77. Find
the integers.
Let f first integer
Assign Labels.
Let f 1 second integer
first integer second integer total
Verbal Model.
f ( f 1) 77
Algebraic Model.
Solve.
The integers are 38 and 39.
Sentence.
Check
?
38 39 77
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Two consecutive odd integers have a sum of 92.
Find the integers.
Let f first integer
Assign Labels.
Let f 2 second integer
first integer second integer total
Verbal Model.
f ( f 2) 92
Algebraic Model.
Solve.
The integers are 45 and 47.
Sentence.
Check
?
45 47 92
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Example 7 Find three consecutive integers whose
sum is 195.
Example 8 Find two consecutive odd integers whose
sum is 96.
Example 9 Find three consecutive even integers
whose sum is -42.
Assign Labels.
Verbal Model.
Algebraic Model.
Solve.
Sentence.
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Example 7 Find three consecutive integers whose
sum is 195.
Assign Labels.
Let f first integer
Let f 1 second integer
Let f 2 third integer
first second third total
Verbal Model.
f ( f 1) ( f 2) 195
Algebraic Model.
Solve.
The integers are 64, 65 and 66.
Sentence.
?
Check
64 65 66 195
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Example 8 Find two consecutive odd integers whose
sum is 96.
Let f first integer
Assign Labels.
Let f 2 second integer
Verbal Model.
first integer second integer total
f ( f 2) -96
Algebraic Model.
Solve.
The integers are -49 and -47.
Sentence.
?
Check
-49 -47 -96
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Example 9 Find three consecutive even integers
whose sum is -42.
Let f first number
Assign Labels.
Let f 2 second number
Let f 4 third number
first second third total
Verbal Model.
f ( f 2) ( f 4) -42
Algebraic Model.
Solve.
The integers are -16, -14 and -12.
Sentence.
?
Check
-16 (-14) (-12) -42
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Homework
2-A6 Pages 95-97 11-26,32-38,47.