Transcript 2.4 Classify and Determine Equation Solutions

2.4 Variables & Equations
Classify Equations and Determine
Solutions
Definitions
Equation: An equation is a mathematical
statement that says one quantity is equal to
another quantity.
Solution: A solution is a value that makes an
equation true (balanced).
Types of Equations
Equations are true, false, or open.
True: 6 + 12 = 18
18 = 18 Of course it’s true.
False: 6 = 4 + 3
6≠ 7 Both sides are not =, the equation is
not balanced
Open: 6y = -3 + 5y
We have no idea if it’s true because we don’t know
the value of y . . . . yet.
.
Test and Classify Each Equation
9–7=3
2≠ 3
False
8+x=2
?
4(5) = 20
20 = 20
Open
True
Writing Equations: Locate
Operational Words
Nine times the opposite of 5 is forty-five
9(-5)
= 45
-45 = 45
Times (of course) is to multiply.
The opposite of 5 is (-5).
Our state of being verb indicates the = sign.
This equation is false.
Write and classify an equation for “twenty minus x is three.”
20 – x = 3
Open
Determining Solutions p. 81
170 + x = 200
Is 30 a solution?
Write, sub, solve
170 + 30 = 200
200 = 200 Yes, 30 is a solution
Is 17 a solution to the equation 9 = y – 10?
9 = 17 – 10
9≠ 7
No, 17 is not a solution to this equation.
Determining Solutions p. 81
8 + t = 2t
Is 1 a solution?
Write, sub, solve
8 + 1 = 2(1)
9≠ 2
No, 1 is not a solution
Is 6 a solution to the equation 9 - m = 3 ?
9-6=3
3=3
Yes, 6 is a solution to this equation.
Check Understanding p. 82
Diving equipment weighs 35 lb. If the diver and the
equipment together weigh 165, could the diver weigh
200 lb?
+
35 +
= 165
200
?
No, 235
= 165
≠ 165
Check Understanding p. 82
A tent weighs 6lb. Your backpack and tent together
weigh 33lb. Use an equation to find if the backpack
weighs 27 lb.
+
6
+
= 33
= 33
27
?
Yes , 33 = 33
Apply the Skill…Work the Process
For each equation, determine if -2 is a solution.
c = -2
24 = 2(c) + 29
8 = 2(c + 6)
c+5 = 3
-2 + 5 = 3
3 = 3
Yes, it is a
solution.
24 = 2(-2) + 29
24 = -4 + 29
24 ≠ 25
No, it’s not a solution.
8 = 2([-2] + 6)
8 = 2(4)
8 =8
Yes, it is a
solution.
Finis
Tomorrow we will begin to solve equations.
Be patient and work the process. The simple
steps will quickly become more complex.