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Solving Linear Equations
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Like Terms
Like terms contain the same variables raised to the same powers.
To combine like terms, add or subtract the numerical coefficients (as appropriate), then multiply the result by the common variable factors.
You can combine like terms by adding or subtracting them (this is not true for unlike terms).
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Combining Like Terms
6x2 + 7x2
19xy – 30xy
13xy2 – 7x2y
13x2
– 11xy
Can’t be combined (since the terms are not like terms)
Examples of Combining Terms
Terms Before Combining After Combining 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
a.) 2(x + y)
= 2x + 2y
Example: Find each product by using the distributive property to remove the parentheses.
b.) 7(x + 2y – 5z) = 7x + 14y – 35z
c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c
a.) 2(x + y)
b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c)
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Remember to keep it balanced by distributing to everyone
Using the Distributive Property
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Addition Property of Equality
If a, b, and c are real numbers, then
a = b and a + c = b + c
are equivalent equations.
Addition Property of Equality
z = – 16 Simplify both sides.
Example:
8 + (– 8) + z = – 8 + – 8 Add –8 to each side.
8 + z = – 8a.)
Keep i
t bala
nced
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Example:
Solving Equations
5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z Use distributive property.
6 – 3z = – 4z Simplify left side.
6 + z = 0 Simplify both sides.
z = – 6 Simplify both sides.
6 – 3z + 4z = – 4z + 4z Add 4z to both sides.
6 + (– 6) + z = 0 +( – 6) Add –6 to both sides.
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Multiplication Property of EqualityIf a, b, and c are real numbers, then
a = b and ac = bc are equivalent equations
Multiplication Property of Equality
Example:– y = 8
y = – 8 Simplify both sides.
(– 1)(– y) = 8(– 1) Multiply both sides by –1.
Balanced
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Divide both sides by 3.3
27
3
3
z
Example:
Using Both Properties
3z – 1 = 26
3z = 27 Simplify both sides.
z = 9 Simplify both sides.
3z – 1 + 1 = 26 + 1 Add 1 to both sides.
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Solving Linear Equations
Solving Linear Equations in One Variable1) 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.