SOLVING ONE-STEP EQUATIONS

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SOLVING ONE-STEP EQUATIONS

• DAY ONE
• Ms. Turk, Algebra I
• Unit 2-1

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New Vocabulary

• Solution the value of the variable that makes
  the equation true
• Equivalent Equations equations that have the
  same solution
• Inverse Operations operations that undo one
  another, like addition and subtraction

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Solving Equations Using Addition and Subtraction

• Think of the equation like a scale. An equation
  is like a scale because it shows that two
  quantities are equal. The scale remains balanced
  when the same weight is added to both sides.

Lets try some examples! Write down all the steps!
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Example 1 Addition
Solve x - 3 8.

• x - 3 3 8 3
• x 11

• Add 3 to each side to get the variable alone on
  one side of the equal sign.
• Simplify.

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Example 2 Addition
Solve -10 x -4.
-10 x -4 10 10 x 6

• Add 10 to each side to isolate the variable on
  one side of the equal sign.
• Simplify.

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Example 3 Addition
Try this one on your own! Solve x - 2.5 6.4.
x - 2.5 6.4 x 8.9

• Did you add 2.5 to both sides?
• Then did you simplify?

2.5 2.5
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Example 4 Subtraction
Solve x 8 -2.
x 8 - 8 -2 - 8 x -10

• Perform the inverse operation to get x by itself
  on one side of the equal sign.
• Simplify.

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Example 5 Subtraction
Solve 3 x -1.
3 x -1 -3 -3 x -4

• Subtract 3 from both sides to get the variable
  alone on one side of the equal sign.
• Simplify.

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Example 6 Subtraction
Try this one on your own! Solve x 3.4 7.7.

• Did you subtract 3.4 from both sides?
• Then did you simplify?

x 3.4 7.7 - 3.4 -
3.4 x 4.3
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Real World Problem Solving
How much does the backpack weigh? A student puts
on his backpack and steps on the scale, which
then reads 156 pounds. He steps on the scale
alone and it reads 134 pounds. Write and solve an
equation to find the weight of the backpack.

• Lets work it out!

• Think Think Think!

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Real World Problem Solving

• Relate
• Define
• Write

• Backpacks weight plus students weight equals
  scale reading.
• Let w backpacks weight.
• w 134 156

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Real World Problem Solving

• w 134 156
• - 134 -134
• w 22
• The backpack weighs 22 pounds.

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Now you try!
Bank Account Balance Kate withdrew 25 from her
savings account. The transaction slip said that
her balance was then 347.88. Write and solve an
algebraic equation to find Kates previous
balance.
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Now you try!

• Relate
• Define
• Write

• Previous balance minus withdrawal equals current
  balance.
• Let p previous balance.
• p - 25.00 347.88

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Now you try!
p - 25.00 347.88 25.00
25.00 p 372.88 Kates previous
balance was 372.88.
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Real World Problem Solving

• This triangle is isosceles so sides AB and BC are
  congruent.

• Find the value of a.
• AB BC
• 16 a - 3.9
• 3.9 3.9
• 19.9 a

B
16
a - 3.9
C
A
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Now you try!

• This triangle is isosceles so sides XY and YZ are
  congruent.

• Find the value of b.
• XY YZ
• b - 37 24
• 37 37
• b 61

Y
24
b - 37
X
Z
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Practice Problems
Please take a few minutes to complete the
following practice problems in your notes.

• n - 2 -5
• c - 4 9
• 28.32 p - 32.96
• -31 26 a
• 5.25 x 3.75
• v - 17 23

• (-3)
• (13)
• (61.28)
• (-57)
• (-1.50)
• (40)