Transcript Simplify/Solve Equations with Varibales on Both Sides

Bell Ringer
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Solve use the DP
5(6+10)
1 ½ x 14
3(x +2)=16
3-5 Solving Equations with the
Variable on Each Side
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Objectives
• Students will solve equations with the
variable on each side.
• Students will solve equations involving
grouping symbols.
Steps for Solving Equations
1. Use the Distributive Property to remove the
grouping symbols. GET RID OF ( )’s
2. Simplify the expressions on each side of the
equals sign.
ADD ALL LIKE TERMS
3. Use the Addition and/or Subtraction Properties of
Equality to get the variables on one side of the
equals sign and the numbers without variables on
the other side of the equals sign. ALL
LETTERS=ALL NUMBERS
4. Simplify the expressions on each side of the
equals sign.ONE LETTER = ONE NUMBER
5. Use the Multiplication and/or Division Property of
Equality to solve. SOLVE THE EQUATION
Example 1
Solve 8 + 5s = 7s – 2
-5s -5s
8 = 2s – 2
+2
+2
10 = 2s
2
2
s=5
Example 2
1/3(18 + 12q) = 6(2q – 7)
6 + 4q = 12q – 42
-4q -4q
6 = 8q – 42
+42
+ 42
48 = 8q
q=6
Example 3
8(5c – 2) = 10(32 + 4c)
40c – 16 = 320 + 40c
-40c
-40c
-16 = 320
No solution
Example 4
4(t + 20) = 1/5(20t + 400)
4t + 80 = 4t + 80
-4t
-4t
80 = 80
All numbers are solutions.
Example 5
8(b + 1) + 4 = 3(2b – 8) – 16
8b + 8 + 4 = 6b – 24 – 16
8b + 12 = 6b – 40
-6b
-6b
2b + 12 = -40
-12 -12
2b = -52
b = -26