Transcript Beginning & Intermediate Algebra. 4ed

Solving Linear
Equations
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Like Terms
Like terms contain the same variables raised to the
same powers.
You can combine like terms by adding or
subtracting them (this is not true for unlike terms).
To combine like terms, add or subtract the
numerical coefficients (as appropriate), then
multiply the result by the common variable factors.
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Combining Like Terms
Examples of Combining Terms
Terms Before Combining
After Combining Terms
6x2 + 7x2
13x2
19xy – 30xy
– 11xy
13xy2 – 7x2y
Can’t be combined
(since the terms are not
like terms)
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Combining Like Terms
We cannot combine
a chicken and a
goat and create a
Chickengoat
It would be
unbalanced!!!
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Combining Like Terms
Or a
Zonkey???
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Using the Distributive Property
Example: Find each product by using the distributive
property to remove the parentheses.
a.) 2(x + y)
b.) 7(x + 2y – 5z)
c.) – 4(3a – 3b – 10c)
a.) 2(x + y) = 2x + 2y
b.) 7(x + 2y – 5z) = 7x + 14y – 35z
c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c
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Using the Distributive Property
Remember
to keep it
balanced by
distributing
to everyone
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Addition Property of Equality
Addition Property of Equality
If a, b, and c are real numbers, then
a = b and a + c = b + c
are equivalent equations.
Example:
a.) 8 + z = – 8
8 + (– 8) + z = – 8 + – 8
z = – 16
Add –8 to each side.
Simplify both sides.
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Solving Equations
Example:
5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z
6 – 3z = – 4z
Use distributive property.
Simplify left side.
6 – 3z + 4z = – 4z + 4z Add 4z to both sides.
6+z=0
Simplify both sides.
6 + (– 6) + z = 0 +( – 6) Add –6 to both sides.
z=–6
Simplify both sides.
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Multiplication Property of Equality
Multiplication Property of Equality
If a, b, and c are real numbers, then
a = b and ac = bc
are equivalent equations
Example:
–y=8
(– 1)(– y) = 8(– 1)
y=–8
Multiply both sides by –1.
Simplify both sides.
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Using Both Properties
Example:
3z – 1 = 26
3z – 1 + 1 = 26 + 1
3z = 27
3 z 27

3
3
z=9
Add 1 to both sides.
Simplify both sides.
Divide both sides by 3.
Simplify both sides.
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Solving Linear Equations
Solving Linear Equations in One Variable
1) Multiply both sides by the LCD to clear the equation of
fractions if they occur.
2) Use the distributive property to remove parentheses if
they occur.
3) Simplify each side of the equation by combining all like
terms.
4) Get all variable terms on one side and all numbers on the
other side by using the addition property of equality.
5) Get the variable alone by using the multiplication
property of equality.
6) Check the solution by substituting it into original
equation.
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