linear equations
TRANSCRIPT
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Solving Linear Equations
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1-step Equations: + and – 2/27/13In elementary school, you solved
equations that looked like this:
In Algebra, we just use a variable instead of the box!
We could rewrite the same equation like this: x + 3 = 5
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To solve:Need to get x by itself.We must “undo” whatever has been
done to the variable.Do the same to BOTH SIDES of the =
sign!Answer should be: x = some number.
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Equations Have to Balance!Both sides of the = sign must “weigh”
the same!When you change one side, do the same
to the other side, so it stays balanced! x + 3 = 7
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Examples:Solve each equation. Check your
answers! x + 3 = -7 m – 6 = 8
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4 + a = -3
-8 + y = 7
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24 = 12 + t
-17 = x – 2
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You Try!Solve each equation. Check your
answers! x – 9 = -6 16 + n = 10
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1-step Equations: × and ÷ 3/11/13Just like with adding and subtracting,
we need to “undo” what is done to x.Use division to “undo” multiplication. Use multiplication to “undo” division.Remember: A fraction bar means
divide!Example: says x divided by 3!
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Examples:Solve each equation:2x = 8
12 = -3b
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You Try!Solve each 1-step equation. -4a = 16
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Basic 2-Step Equations 3/13/13A lot like 1-step equations!Goal: Get x by itself!Need to “undo” what is done to x.Always do the same thing to BOTH SIDES!Use Order of Operations backwards:
Add/Subtract firstMultiply/Divide last
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Examples:4x + 7 = 27 – 6 – 2y = 10
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5 = 7r - 2 -4 = 2 - m
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You Try!Solve each equation. Check your
answers!-3x + 7 = 16 -8 = 2a + 2
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Multi-Step Equations 3/18/13Multi-step equations have ( ).To solve:
Distribute first!!Then, solve like a 2-step equation!
Example: 4(-x + 4) = 12
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Examples:3(– 6 + 3x) = 18
30 = -5(6n + 6)
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10 (1 + 3b) = -20
-2 = -(n – 8)
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Your Try!-6(1 – 5v) = 54
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2 Variables- Same Side 3/21/13Some equations have variables in more
than one place.When variables are on the same side
of the = sign:First, Combine Like Terms
Like terms may NOT cross the = sign!Then, solve like a 2-step
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Examples:2x + 3x + 1 = 36
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3 + 6x – 2x = -5
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-26 = -7x + 6 + 3x
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You Try!Solve for x.8x – 3x + 7 = 17
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Variables on Both Sides 3/22/13To solve equations like this:
2x – 4 = 2 + 5x1. Get variables together on the left.
Add or subtract right side x term from both sides.
2. Solve like a 2-step equation.
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Examples9 – 7x = -5x – 7
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-3x – 7 = 2x – 13
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You Try!-3x + 9 = 44 + 4x