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1.7 Intro to Solving Equations
Objective(s):
1.) to determine whether an equation is true,
false, or open
2.)to find solutions sets of an equation
3.)to recognize equivalent equations
Vocabulary
Equation: Mathematical sentence that uses an
equal sign to state that two expressions
represent the same number.
3 types of Equations:
True: 3 + 7 = 10
False: 3 – 7 = 10
OPEN: equation that contains at least one
variable: m + 9 = 210
Vocabulary
Solution: a replacement number for
a variable that makes an equation
true. 5 is a solution for the
equation x + 3 = 8.
Solution Set: The collection of all
solutions to an equation
To see if a given number is a
solution for an equation…
• Substitute the number in for the variable
• If right= left then it is true
• If right left then it is false
Ex 1: Is 7 a solution for the equation
3k + 2 = 23
3 • 7 + 2 = 23 is
TRUE
Ex 2: Is 6 a solution for the equation
5r – 9 = 17
5 • 6 - 9 = 21
Not a solution
To solve for the given
replacement set…
• Plug all numbers given in the replacement
set into the equation
• Which ever # makes the right=left is the
correct answer.
Ex 3: Solve for the given
replacement set:
3x 5 323,6,9
Substitute each number to
find which one(s) work.
3 9 5 32
Ex 4: Solve for the given
replacement set:
5x 3 282,5,8
5 5 3 28
Equivalent Equations
Two equations are equivalent if one
can be changed into the other by:
Add the same number to both sides of
the equation.
Subtract the same number from both
sides.
Multiply both sides by the same
number.
Divide both sides by the same number
Ex 5:Each pair of equations is
equivalent. What was done to the
first equation to get the second one?
x+2=5
x + 7 = 10
Added 5 to both sides
Ex 6: Each pair of equations is
equivalent. What was done to the
first equation to get the second one?
k-4=7
k = 11
Added 4 to both sides
Homework
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