Name______________________________
Date: _________________ Block:_______
Ms. Gallagher
Warm – Up Put each of the following equations into slope – intercept form
(y = mx + b)
1. 2x + y = 10
3. –12x + 4y = –16
2. 3x – 6y = 12
4. 3x + 8y = 12
Notes Rewriting Formulas and Equations
A ______________ is an equation that relates two or more quantities, usually represented
by variables. What are some formulas that you know?
To SOLVE FOR A VARIABLE means to rewrite an equation so the given variable is isolated
on one side and does not appear on the other.
EXAMPLE ONE Solve for the given variable
Solve the equation C = 2πr for the radius.
What is the radius if the circumference is 44 inches?
EXAMPLE TWO Solve for the given variable
Solve the equation P = 2L + 2W for W.
YOU TRY Solve for the given variable
a) Solve the equation A = bh for b.
c) Solve the equation A = bh for h.
b) What is the base if the area is 12
inches and the height is 2 inches?
d) What is the height if the area is 35
inches and the base is 7 inches
The absolute value of a number x, |x|, is the distance that number is away from zero.
Expression:
Meaning:
|x| = k
The distance between x and zero is k.
|x – 0| = k
The distance between x and zero is k.
|x – b| = k
The distance between x and b is k.
When solving absolute value equations, we need to set up 2 equations. The first
equation will look the same, the other equation will have the opposite solution.
EXAMPLE ONE Solve the Absolute Value equation and graph the solution.
|x – 5| = 7
YOU TRY Solve the Absolute Value equation and graph the solution.
|5x – 10| = 45
Sometimes, we will get a solution that does not satisfy the original equation. This is
called an extraneous solution and we must throw it out!
EXAMPLE TWO Checking for extraneous solutions
|2x + 12| = 4x
YOU TRY Check for extraneous solutions
|2x + 5|= 3x
This is why you ALWAYS ALWAYS
ALWAYS check your answers!!
Homework
1.4 # 7, 8, 9, 10, 11, 12, 18, 21
1.7 # 5, 8, 9 – 13, 21, 22, 23, 31, 34, 35, 36