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1.3 Solve Linear Equations
Goal  Solve linear equations.
Your Notes
VOCABULARY
Equation
A statement that two expressions are equal
Linear equation
A linear equation in one variable is an equation that can be written in the form ax + b = 0,
where a and b are constants and a  0.
Solution
A number is a solution of an equation in one variable if substituting the number for the
variable results in a true statement.
Equivalent equations
Two equations are equivalent equations if they have the same solution(s).
TRANSFORMATIONS THAT PRODUCE EQUIVALENT
EQUATIONS
_ Addition_Property
of Equality
Add the same number to
each side.
If a = b, then a + c = b + c.
Subtraction Property
of Equality
_Subtract_the same
number from each side.
If a = b, then a  c = b  c.
Multiplication
Property of Equality
Multiply each side by the If a = b and c  0, then
same nonzero number.
_a  c_ = _b  c_
Division Property of
Equality
_Divide_ each side by the If a = b and c  0, then
same nonzero number.
a  c = b  c.
Your Notes
Example 1
Solve an equation with a variable on one side
Solve
3
x  15  33.
4
Solution
3
x  15  33.
4
3
x  _18_
4
Write original equation.
Subtract _15_ from each side.
x  4 (18)
3
4
Multiply each side by
, the
3
3
reciprocal of
4
x = _24_
Simplify.
The solution is _24_.
CHECK Check x = _24_ in the original equation.
3
3
x  15 
( 24 ) + 15 = _18_ + 15 = _33_
4
4
Checkpoint Solve the equation. Check your solution.
1. 15a  6 = 9
a=1
2.
5
y  3  13
6
y = 12
Your Notes
Example 2
Solve an equation using the distributive property
3(3x  2) = 7(4x + 3)  31x
Original equation
_9x_ 6 = _28x_ + 21  31x
Distributive property
9x  6 = _3x_ + 21
Combine like terms.
_12x_  6 = 21
Add _3x_ to each side.
12x_ = _27_
9
.
x=
4
Add _6_ to each side.
The solution is
Divide each side by _12_ and simplify.
9
4
CHECK Check x =
9
in the original equation.
4
9
 9
  9

3  3   2  ? 7  4   3   31 
4
4
4

 

Substitute in for x.
279
 19 
3  ? 7(12) 
4
4
Simplify.
57 57

4
4
Solution checks.
Checkpoint Solve the equation. Check your solution.
3. 4(x 6) = 3(x + 2)
x = 30
4. 3(x + 4) = 2(x 7) 15x
1
x
10
Home work
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