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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  323,6,9
Substitute each number to
find which one(s) work.
3  9  5  32
Ex 4: Solve for the given
replacement set:
5x  3  282,5,8
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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