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LESSON 3.1 Notes Day 3- Solving Equations Using Addition or Subtraction
Goal: Solve equations using addition or subtraction.
Warm-up: Video on inverse operations.
Vocabulary
Equivalent equations:
Inverse operations:
Subtraction Property of Equality
Words Subtracting the same number from each side of an equation produces an equivalent
equation.
Numbers If x + 9 = 12, then x + 9 – 9 = 12 – _____ .
Algebra If x + a = b, then x + a – a = _____ – a.
EXAMPLE 1 - Solving an Equation Using Subtraction
Solution
a) x + 7 = 13
CHECK!
b) -9 = y + 20
Addition Property of Equality
Words Adding the same number to each side of an equation produces an equivalent equation.
Numbers If x – 6 = 1, then x – 6 + 6 = 1 + _____.
Algebra If a = b, then a +_____ = b + c.
EXAMPLE 2 - Solving an Equation Using Addition
Solution
a) x - 9 = 15
CHECK!
b) -11 = y - 15
1
Now You Try It! Solve the equation. Check your solution.
Solution
CHECK!
1) y + 4 = 13
2) –17 = 7 + t
3) n – 11 = 14
4) –2 = s – 3.5
EXAMPLE 3 – Simplifying an Equation first.
Solution
a) x + (-4) = 25
CHECK!
b) x – (-9) = -30
Now You Try It! Solve the equation. Check your solution.
Solution
CHECK!
5) y + (-5) = -10
6) –13 = t – (-3)
2
Solution
CHECK!
7) x – (-10) = 14
8) n + (-3) = 20
EXAMPLE 4 - Using a Model
Kites You are flying a kite. The total length of the kite's string is 275 feet. So far you have let
out 153 feet of string. Write and solve an equation to find out how much string do you have left.
Let s represent the length of string left. Write a verbal model (in words).
=
+
Length of string
already let out
Think: What
part of the
verbal model is
missing? What
values
correspond to
each part of the
verbal model?
________=
_______ +153
Write an algebraic model.
Subtract
from each side.
Simplify, s is by itself.
ANSWER :
3