Chapter 1 - Review
Company A - $50 initial set-up fee and $1.50 per brochure Company B - $75 initial set-up fee and $1.00 per brochure Write an equation for each company and find out how many brochures you would need to print for the cost from each company to be equal
50 brochures
Rule or Theorem
A proven conjecture or statement
Solution
A value that makes the equation true
Extraneous Solution
An apparent solution that must be rejected because it does not satisfy the original equation
Linear Equation in One Variable
An equation that can be written in the form ax + b = 0, where a and b are constants and a does NOT equal 0
Absolute Value Equation
An equation that contains an absolute value expression
Literal Equation
An equation that has two or more variables
Identity
An equation that is true for all values of the variable
Equivalent Equations
Equations that have the same solution(s)
Solve 5(1 + x) = 5x + 5
Identity - Infinitely Many Solutions
Solve 5(2c + 7) - 3c = 7(c + 5)
Infinite Solutions
13 + 3p + 10 = 23 + 3p
Infinite Solutions (Identity)
The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Use "v" for the unknown.
Iv - 84.5I = 10.5
Formula
Shows how one variable is related to one or more variables. This is a type of Literal Equation
Equation
Statement that two expressions are equal
Mean
The average of the numbers: a calculated "central" value of a set of numbers
Inverse Operations
Two operations that undo each other, such as addition and subtraction
Conjecture
Unproven statement about a general mathematical concept
Solve x + 2 = 5
X = 3
Quadrilateral - Sum of ALL angles = 360 Angle 1 - 5b Angle 2 - 4b Angle 3 - 5b Angle 4 - 4b Solve for b
b = 20
Solve Ib - 12I = 15
b = 27; b = -3
Solve |2b - 9| = |b - 6|
b = 3; b = 5
Solve g + 5 = 17
g = 12
y = mx + b - Solve for m
m = (y-b)/x
If m = pV and p = 5.01g/cm^3 and V = 1.2cm^3 - What is the mass (m)
m = 6.012g
p = m/V - solve for m
m = Vp
Solve 3n - 3 = 4n +1
n = -4
Solve 5n = -20
n = -4
Solve n + 5n + 7 = 43
n = 6
Solve I2r + 5I = 3r
r = 5; r = -1 is an extraneous solution
Solve 2.6 = -0.2t
t = -13; Divide each side by -0.2
Solve Ix - 2I = I4 + xI
x = -1
Solve x - 5 = -9
x = -4
Triangle - Sum of ALL Angles = 180 Angle 1 = 5x Angle 2 = 90 Angle 3 = x Solve for x
x = 15
Solve -6x + 23 + 2x = 15
x = 2
Solve 4x + 8 + 6x - 5 = 33
x = 3
Solve 4x = 12
x = 3
Solve I2x + 6I = 4x
x = 3, x = -1 is extraneous
Solve Ix - 5I = 3
x = 8 and x = 2
Solve 2(y - 4) = -4(y + 8)
y = -4
Solve 3y + 11 = -16
y = -9
2x - 4y = 20 - Solve for y
y = 1/2x - 5
Solve Iy + 3I = 17
y = 14, y = -20
Solve for y 5x + y = 2
y = 2 - 5x
8x - 3 = 5 + 4y - Solve for y
y = 2x - 2
Solve for y 2x + 5y = 3y + 8
y = 4 - x
Solve 7 + 4y = 39
y = 8
Solve z + 3 = -6
z = -9; Subtract 3 from each side
Solve z/4 = 12
z = 48
For a school play, the maximum age for a youth ticket is 18 years old. The minimum age is 10 years old. Write an absolute value equation for which the two solutions are the minimum and maximum ages for a youth ticket.
|x - 14| = 4