Download Solving Equations

Solving Equations
Recall that the solution to an
equation is any value for the
variable that makes the equation
true.
t = 4 is the solution of t + 2 = 6
Goal: apply the addition and
multiplication principles to
solve equations by isolating
the variable.
Examples: Verify that the given
values are solutions to the equations.
1. x + 8 = 10 when x is 2
2. x + 8 = 6 when x is –2
3. 2y = 14 when y is 7
The equations:
x = –2 and x + 8 = 6
are both true when x is –2.
Equations that have the same solution
are called equivalent equations.
To solve an equation –
1. Use algebra principles.
2. Isolate the variable.
The rules of algebra allow us to
change an equation without changing
the solution.
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The Addition Principle:
For real numbers a, b, and c,
a = b is equivalent to a + c = b + c.
Adding the same number to both
sides of an equation does not change
the solution.
Examples: Use the addition principle
to isolate the variable and solve.
1. x + 8 = 6
2. 9.5 = w – 1.1
The Multiplication Principle:
For real numbers a, b, and c, with
c ≠ 0,
a = b is equivalent to a . c = b . c
Multiplying both sides of an
equation by the same, nonzero
number does not change the
solution.
Note: The multiplication principle can
act just like a division principle:
For a, b, and c real numbers, c ≠ 0,
if a = b, then
a b
1
1
.
=
⋅ a = ⋅ b or
c
c
c c
Example: Use the multiplication
principle to isolate the variable and
solve:
2x 1
=
3 4
Examples: Use the
multiplication principle to
isolate the variable and solve:
1. 2x = 14
2. 1.2t = 36
2
Examples: Choose the correct
principle to isolate the variable and
solve.
2 u
1. 7 = 3
2. 3 + v = 19
3. 1.4 = x – 0.5
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