Download Algebra 1 Lesson Notes 3.4

Algebra 1
Lesson Notes 3.4
Date ________________
Objective: Solve equations with variables on both sides.
 I/N, eliminate fractions by multiplying BOTH SIDES of the equation by
the common denominator.
 I/N, eliminate grouping symbols by using the distributive property
SHUFFLE
 I/N, simplify each side of the equation by combining like terms.
 Collect the variable terms on one side of the equal sign and the constants on
the other side of the equal sign by using the properties of equality.
DIVIDE
SIMPLIFY
Steps for Solving Linear Equations
 If the coefficient of the variable is not 1, divide both sides of the equation by
the coefficient.
THINK: Is there anything to SIMPLIFY … Is there anything to SHUFFLE … Is there
anything to DIVIDE !
Example 1 (p154): Solve an equation with variables on both sides
a.
Solve: 7  8 x  4 x  17
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 Check your answer!
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b.
Solve: 13 + 5x   x  
Example 2 (p154): Solve an equation with grouping symbols
a.
1
4
Solve: 9 x  5  16 x  60 
 Check your answer!
Note: There is often more than one
way to solve an equation.
Try it:
−5(a – 1) = 11 – 6a
5( x  3)  2  2(3x  4)
Example 3 (p 155): Solve a real-world problem
a.
A car dealership sold 78 new cars and 67 used cars this year. The number of new cars
sold has been increasing by 6 cars each year. The number of used cars sold has been
decreasing by 4 cars each year. If these trends continue, in how many years will the
number of new cars sold be twice the number of used cars sold?
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b.
A music website sold 94 single songs and 67 albums this week. The number of single
downloads has been increasing by 22 each week. The number of album downloads has
been decreasing by 5 each week. If these trends continue, in how many weeks will the
number of single downloads be 10 times greater than the number of album downloads?
Equations do not always have exactly one solution. Some equations have an infinite number of
solutions. Some equations have no solutions at all.
Identity: an equation that is true for all values of the variable. The solution for an identity is
all real numbers.
If solving an equation results in a statement that is always true (e.g. 6 = 6), the
equation has an infinite number of solutions. The solution is ‘All real numbers’.
If solving an equation results in a statement that is always false (e.g. 0 = − 4), the equation
has no solutions. The solution is ‘No solution’.
Example 4 (p 156): Identify the number of solutions of an equation
a.
Solve, if possible: 5x  6  5 x 1
b.
Solve, if possible: 4 3x  2  2  6 x  4
 HW:
A4a
A4b
Prepare for Quiz 3.3-3.4
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