Name___________________________________________ Date_________________________ Algebra I – Pd ____ 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 = -15 1st – combine like terms 4x + 21 = -15 Now it looks like a multistep equation that we already did -21 -21 2nd – Use subtraction to get rid of the addition. 4x = -36 3rd –Divide to get rid of the multiplication 4 4 x = -9 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___________________________________________ Date_________________________ Algebra I – Pd ____ 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 2) 22 4x = 12x + 126 3)

4) 5(2x + 14) = 2(3x + 31) 5) 12(3x + 4) = 6(7x + 2) 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) = 35 – x

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

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Absolute Value Equations 2C

Solving Absolute Values Vocabulary: Opposite Numbers are two different numbers that have the same absolute value. Example: and 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) = 2) = 3) = 4) = 5) =

6) = 7) = 8) = 9) = 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.

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___________________________________________ Date_________________________ Algebra I – Pd ____ 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) _______ _______ _______ _____________________________

2) _______ _______ _______ ______________

3) _______ _______ _______ ______________

4) _______ _______ _______ ______________

5) _______ _______ _______ ______________

6) _______ _______ _______ ______________

7) _______ _______ _______ ______________

Name___________________________________________ Date_________________________ Algebra I – Pd ____ Graphing Absolute Values 2D (2)

1) _______ _______ _______

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2) _______ _______ _______

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Name___________________________________________ Date_________________________ Algebra I – Pd ____ Absolute Value Multiple Choice 2E

Absolute Value Multiple Choice Questions _____ 1) If , what is the value of when ?

(1) (2) (3) (4) _____ 2) If what is the value of when ?

(1) (2) (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) (4) _____ 5) What statement is true about the graphs of and ?

(1) The graphs coincide. (2) The graph of is the refection of the graph of in the . (3) The graph of is the refection of the graph of in the . (4) The graph have exactly one point in common. _____ 6) What is the vertex of:

(1) (2) (3) (4) _____ 7) What is the vertex of:

(1) (2) (3) (4)

_____ 8) What is the vertex of:

(1) (2) (3) (4) _____ 9) What is the vertex of:

(1) (2) (3) (4) _____ 10) What is the vertex of:

(1) (2) (3) (4) Name___________________________________________ Date_________________________ Algebra I – Pd ____ Graphing Absolute Values 2F Directions: Show all work necessary in the spaces provided to graph the absolute value equation. 1)

_______ _______ ____________________________

2)

_______ _______ ____________________________

3)

_______ _______ ____________________________

4)

_______ _______ ____________________________