Download p-value number sentence truth value let p = 0 let p = 4 let p = 1 + 2

Aim #9: How do we determine solution sets for equations and inequalities?
Homework: Handout
9-22-16
Do Now: Consider the equation 7 + p = 12. Complete the table below for the values
of p that are given.
p-value
number sentence
truth value
let p = 0
let p = 4
let p = 1 + 2
let p = 5
Is a table necessary for this question? Is it obvious what value(s) we could assign to
p to make the equation true?
The ___________ _____ of an equation written with only onevariable is the set
of all values one can assign to that variable to make the equation a true statement.
Any one of those values is said to be a solution to the equation.
To solve an equation means to find the solution set for that equation.
a. Why should the equations (x - 1)(x + 3) = 17 + x and (x - 1)(x + 3) = x + 17 have
the same solution set?
b. Why should the equations (x - 1)(x + 3) = 17 + x and (x + 3)(x - 1) = 17 + x have
the same solution set?
c. Should the equations (x - 1)(x + 3) - 500 = 17 + x and (x - 1)(x + 3) = 517 + xhave
the same solution set? Why?
d. Should the equations (x - 1)(x + 3) = 17 + x and 3(x - 1)(x + 3) = 51 + 3x
have the same solution set? Why?
If x is a solution to an equation, then it will also be a solution to any new
equation we make by applying any real number property to the expression
in that equation.
Use the commutative property to write an equation that has the same solution set
2
as x - 3x + 4 = (x + 7)(x - 12)(5).
Use the associative property to write an equation that has the same solution set
2
as x - 3x + 4 = (x + 7)(x - 12)(5).
Does this reasoning apply to the distributive property as well?
What properties did parts c and d above rely on? ________________________
Addition Property of Equality: ______________________________________
If a = b is true, then a + c = b + c will also be true for all real numbers
Multiplication Property of Equality: __________________________________
If a = b is true, then ac = bc will also be true for all real numbers
Think about this ...
Suppose I see the equation |x| + 5 = 2, is it true, then, that |x| + 5 - 5 = 2 - 5?
Solve the following equations and name the properties used for each step:
2. 2(s + 5) = 30
1. 2r + 3 = 1
4
3. 4y - 3 = 5y - 8
4. 7x – 3 – (x – 11) = 4(x + 6)
Consider the equation in #3 above. Does it matter which step happens
first: subtract 4y from both sides, add 3 to both sides, subtract 5y from both
sides, or add 8 to both sides?
5. Determine which of the following equations have the same solution set by
recognizing properties, rather than solving.
a. 2x + 3 = 13 - 5x
b. 6 + 4x = -10x + 26
d. 0.6 + 0.4x = -x + 2.6
e. 3(2x + 3) = 13 - x
5
g. 15(2x + 3) = 13 - 5x
h. 15(2x + 3) + 97 = 110 - 5x
c. 6x + 9 = 13 - x
5
f. 4x = -10x + 20
Let's sum it up!!!
When we need to find the solutions of an equation, we should use the _______________,
_______________ & __________________ properties and the properties of
________________ to create an equivalent, but simplified equation which can be easily
solved.