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Algebra I – Pd ____
Date_________________________
Complex Equations
2A
Equations with more than one x on the same side of the equal sign:
You need to simplify (combine like terms) and then use the same steps as a multi-step equation.
9x + 11 – 5x + 10
4x + 21
-21
4x
4
x
= -15
= -15
-21
= -36
4
= -9
1st – combine like terms
Now it looks like a multistep equation that we already did
2nd – Use subtraction to get rid of the addition.
3rd –Divide to get rid of the multiplication
Then we check the answer by putting it back in the original equation:
9 (-9) + 11 – 5(-9) + 10 = -15
-81 + 11 + 45 + 10 = -15
- 15 = - 15
Directions: Solve the Multi-Step Equations in your notebook and check! No work = No credit
1) 15x – 24 – 4x = – 79
2) 102 = 69 – 7x + 3x
3) 3x + 15 + 4x = – 13
4) 3(4x – 5) + 2(11 – 2x) = 43
5) 9(3x + 6) – 6(7x – 3) = 12
6) 7 – 3(x – 1) = – 17
7) 5(3a + 1) – 2(a + 1) = 7
8) 3(3x + 1) – 8x = 19
9) 5 = 4(3 + x) – 5x
10) 2(3x – 5) + 12 = 0
11) 7(4x – 5) – 4(6x + 5) = –91
12) 3(1 – 2x) + 8 = – 13
13) 3(2y + 5) – 8y = 1
14) 3(2x - 5) – 4x = 33
15) 3m + 2(8 – m) = 3
Name___________________________________________
Algebra I – Pd ____
Date_________________________
Complex Equations (2)
2B
Equations with x's on BOTH sides of the equal sign:
You need to "Get the x's on one side and the numbers on the other." Then you can solve.
Example:
12x – 11 = 7x + 9
-7x
-7x
1st – Move the x’s to one side. (move the “x” to the left)
5x – 11 = 9
2nd – Move the integer numbers to the other side (move to the right)
+11 +11
3rd – Now divide to isolate the variable
5x = 20
5
5
x=4
We check the answer by putting it back in the original equation:
Check:
12x – 11 = 7x + 9
We have that x = 4
12(4) – 11 = 7(4) + 9
48 – 11 = 28 + 9
37 = 37 (It checks!)
Directions: Solve the Multi-Step Equations in your notebook and check! No work = No credit
1) 11x
3 = 7x + 17
4) 5(2x + 14) = 2(3x + 31)
2) 22
4x = 12x + 126
5) 12(3x + 4) = 6(7x + 2)
3)
6) 3x
25 = 11x
5 + 2x
7) 2x – 5(x + 1) = 3x + 1
8) –(x + 7) = 3x + 5
9) 5(x + 1) – 3(2x + 5) = 2(10 + x) + 3
10) 4x + 9 = 2(x – 3) + 5
11) 9b = 2b – 3(8 – b)
12)
13) 5(6 – p) = – 3(p + 2)
14) 3(4c – 7) = 2(3c + 11) +5
15) 3.3 – m = 3(m – 1.7)
16) 8x – 3 = 3(3x – 4)
17) 2x + 10 – x – 22 = 3(x + 4)
18) 4y + 3(2y – 4) = y – 1
19) 5(3a+ 1) – 2(a + 1) = 7
20) 3x + 5 + 2x = 4(3 + x)
21) 3(3x + 1) = 8x + 19
= 35 – x
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Algebra I – Pd ____
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Absolute Value Equations
2C
Solving Absolute Values
Vocabulary: Opposite Numbers are two different numbers that have the same absolute value. Example:
are opposite numbers because
and
.
1) When opposite numbers are added, the sum is zero.
2) To get the opposite of a number, change the sign.
3) The absolute values of opposite numbers are the same.
4) Opposite numbers are equidistant from 0 on a number line.
Absolute Value: Evaluate the following.
1)
6)
=
2)
=
7)
=
3)
=
8)
=
4)
=
9)
=
5)
=
10)
Directions: Use the number lines to find the opposite of the plotted point. Plot the opposite of the given
number using your red pen.
=
=
and
Solving Absolute Value Equations
Solving absolute value equations is almost the exact same as solving regular equations with one major
difference. In most cases you have 2 solutions.
How to solve absolute value equations
1) Isolate the absolute value.
2) Split into two separate equations, setting one to the negative and one to the positive.
3) Solve for x in both equations.
4) Check both of your solutions in the original equation.
Example:
Steps:
1) Isolate the absolute value: ** The steps are the same as if you were
getting the x by itself. You move away all other numbers by doing
the opposite operation:**
2) Now split into two separate equations. Notice that we have
dropped the absolute value bars! Now solve the two different
equations for “x”
CHECKS:
3) Check by substituting both answers
back into the original equation.
Directions: Solve and CHECK the following absolute value equations in your notebook. No work = No credit!
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
Name___________________________________________
Algebra I – Pd ____
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Graphing Absolute Values
2D
The standard form for an absolute value equation is:
____________________ of the absolute value graph
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_______________________ of the absolute value graph
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_______________________ of the absolute value graph
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Examples:
1)
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2)
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3)
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4)
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5)
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6)
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7)
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Name___________________________________________
Algebra I – Pd ____
1)
Date_________________________
Graphing Absolute Values
2D (2)
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2)
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Name___________________________________________
Algebra I – Pd ____
Date_________________________
Absolute Value Multiple Choice
2E
Absolute Value Multiple Choice Questions
_____ 1) If
, what is the value of
(1)
_____ 2) If
when
(2)
what is the value of
(1)
?
(3)
when
(2)
(4)
?
(3)
(4)
_____ 3) When graphed on the same set of axes, in how many different points do the graphs of
and
intersect?
(1)
(2)
(3)
(4)
_____ 4) When graphed on the same set of axes, in how many different points do the graphs of
and
intersect?
(1)
(2)
(3)
_____ 5) What statement is true about the graphs of
(4)
and
?
(1) The graphs coincide.
(2) The graph of
is the refection of the graph of
(3) The graph of
is the refection of the graph of
(4) The graph have exactly one point in common.
in the
in the
_____ 6) What is the vertex of:
(1)
(2)
(3)
(4)
(3)
(4)
_____ 7) What is the vertex of:
(1)
(2)
.
.
_____ 8) What is the vertex of:
(1)
(2)
(3)
(4)
(3)
(4)
_____ 9) What is the vertex of:
(1)
(2)
_____ 10) What is the vertex of:
(1)
(2)
(3)
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Algebra I – Pd ____
(4)
Date_________________________
Graphing Absolute Values
2F
Directions: Show all work necessary in the spaces provided to graph the absolute value equation.
1)
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2)
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3)
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4)
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