1, 2, Multi-Step
m - 2 = 13
m - 2 = 13
+2 +2
m = 15
What are the three types of solutions you may find when solving algebra equations?
One solution
No solution
Infinite solutions
What is the math term describing "x" in the equation: 5x + 3 = 52
Which of the following is a LITERAL equation?
14y = 63
2c + 47 = -4 - 9(3c + 4)
tx = r + s
tx = r + s
Solve for y:
1 + 4y = 8x - 7
1 + 4y = 8x - 7
-1 -1
4y = 8x - 8
Divide, Divide, Divide!
y = 2x -2
4.3 + x/4 = 2.2
4.3 + x/4 = 2.2
-4.3 -4.3
4(x/4) = (-2.1)4
x = -8.4
What is the solution of an equation when the result is 4 = 4 ?
Infinite
Addition is the _________ operation of subtraction, while division is the ________ operation of multiplication.
Hint: It begins with the letter "I"
Inverse
Isolate, or solve for, a:
as = px
a = px/s
Solve for y:
y - 10 = 2(x - 1)
y - 10 = 2(x - 1)
y - 10 = 2x - 2
+10 +10
y = 2x + 8
-88 = -4(-3b + 7)
-88 = -4(-3b + 7)
-88 = 12b - 28
+28 +28
-60 = 12b
divide both sides by 12...
b = -5
Give an example of an answer that describes "NO SOLUTION"
5 = 2 or any equation that IS NOT TRUE
The _______ term is the one that does not include a variable. It is a number "standing alone." Example: The "4" in the equation -3x + 4 = 19
Constant
Solve for the indicated variable:
q = -n + a, for a
q + n = a OR a = q + n
Solve for y:
6y + 18 = 18x
6y + 18 = 18x
-18 -18
6y = 18x - 18
Divide, Divide, Divide!
y = 3x - 3
-8(10x - 10) = 6(12x - 12)
-8(10x - 10) = 6(12x - 12)
-80x + 80 = 72x - 72
+80x +80x
80 = 152x - 72
+72 +72
152 = 152x ...divide both sides by 152
x = 1
Solve for x:
5(4x + 9) = 5(4x + 9)
Hint: Does this have a solution?
Infinite Solutions
What is our GOAL when given the equation:
7x + 9 - 3 = -14x - 40(3 + 7)
Isolate the variable x
True or False?
rx + e = ta is equal to ta = rx + e
True
Solve for y:
18x + y - 12x = 7
18x + y - 12x = 7
6x + y = 7
-6x -6x
y = -6x + 7
In February, Amy's cell phone bill was $6 more than 1/3 of her car payment. If the cell phone bill was seventy three dollars, what was the car payment?
6 + 1/3c = 73
-6 -6
1/3c = 67
3(1/3c) = (67)3
c = 201
Solve for r:
-8 + 4(r - 11) = 2(2r - 7)
-8 + 4(r - 11) = 2(2r - 7)
-8 + 4r - 44 = 4r - 14
-52 + 4r = 4r - 14
-4r -4r
-52 = -14 NO SOLUTION
Identify the type of "math problem" you have when given: 2x + 9/8 = 8(4x - 3)
Algebraic Equation
Evaluate:
b + c * 14, when b = 2 and c = -7
b + c * 14
2 - 7 * 14
2 - 98 = -96
Solve for y:
7x - y = 14 + 9x
7x - y = 14 + 9x
-7x -7x
-y = 2x + 14
y = -2x - 14