Solving Equations Using Addition and Subtraction

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Solving Equations Using Addition and Subtraction
Objectives

• A.4f Apply these skills to solve practical
  problems.
• A.4b Justify steps used in solving equations.
• Use a graphing calculator to check your
  solutions.

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To Solve an Equation means...

• To isolate the variable having a coefficient of 1
  on one side of the equation.
• Ex x 5 is solved for x.
• y 2x - 1 is solved for y.

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Addition Property of Equality

• For any numbers a, b, and c, if a b, then a c
  b c.

What it means
You can add any number to BOTH sides of an
equation and the equation will still hold true.
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An easy example

• Would you ever leave the house with only one shoe
  on?
• Would you ever put blush on just one cheek?
• Would you ever shave just one side of your face?

• We all know that 7 7.
• Does 7 4 7? NO!
• But 7 4 7 4.
• The equation is still
• true if we add 4
• to both sides.

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Lets try another example!

• Always check your solution!!
• The original problem is x - 6 10.
• Using the solution x16,
• Does 16 - 6 10?
• YES! 10 10 and our solution is correct.

• x - 6 10
• Add 6 to each side.
• x - 6 10
• 6 6
• x 16

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What if we see y (-4) 9?

• Check your solution!
• Does 13 - 4 9?
• YES! 99 and our solution is correct.

• Recall that y (-4) 9
• is the same as y - 4 9.
• Now we can use the addition property.
• y - 4 9
• 4 4
• y 13

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How about -16 z 7?

• Remember to always use the sign in front of the
  number.
• Because 16 is negative, we need to add 16 to both
  sides.
• -16 z 7
• 16 16
• z 23

• Check you solution!
• Does -16 23 7?
• YES! 7 7 and our solution is correct.

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A trick question...

• -n - 10 5
• 10 10
• -n 15
• Do we want -n? NO, we want positive n.
• If the opposite of n is positive 15, then n must
  be negative 15.
• Solution n -15

• Check your solution!
• Does -(-15)-105?
• Remember, two negatives a positive
• 15 - 10 5 so our solution is correct.

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Subtraction Property of Equality

• For any numbers a, b, and c, if a b, then a - c
  b - c.

What it means

• You can subtract any number from BOTH sides of an
  equation and the equation will still hold true.

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3 Examples

• 1) x 3 17
• -3 -3
• x 14
• Does 14 3 17?
• 2) 13 y 20
• -13 -13
• y 7
• Does 13 7 20?

• 3) z - (-5) -13
• Change this equation. z 5 -13
• -5 -5
• z -18
• Does -18 -(-5) -13?
• -18 5 -13
• -13 -13 YES!

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Try these on your own...
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The answers...