Solving Equations! {with decimals}

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Solving Equations! with decimals

• U2L11
• PS2 Solve single- and multi-step word problems
  involving operations with fractions and decimals
  and verify the solutions

DO NOW JJ is baking a cake. He wants to double
the recipe so he has enough to share with the
whole class. The recipe calls for 3 ½ cups of
flour. First he added 1 ¾ cup and later he added
2 ½ cups. How many more cups of flour does he
need?
Planner Hw p. 216 -217 9, 22, 23, 38, 40, 41
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What is an equation?

• Equation a mathematical statement that two
  things are equal.
• It consists of two expressions, one on each side
  of an 'equals' sign.
• We know the left side and right side are equal

Equations are like a balance scale
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Solving an equation -- Terminology

• Solving the equation The process of finding
  the value of the variables
• We say "solve for x" - meaning solve the equation
  to find the value of the unknown number x that
  makes the statement true
• In order to solve for x, we must isolate the
  variable
• (We need to get x alone on one side of the equal
  sign)
• Goal is to end up with x something

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How to solve equations

• To get x alone UNDO every operation that is
  happening to x
• UNDO ? perform the opposite operation
• Do PEMDAS in reverse! (add/subtract first, then
  multiply/divide, etc)
• Whatever you do to an equation,do the   S A M E
    thingto   B O T H   sides of that equation!
• Keep the scale balanced
• Example
• x 4.5 23.2
• -4.5 -4.5
• x 18.7

• 4.5 is being added to x, so we UNDO the operation
  by doing the opposite operation
• Subtract 4.5 from BOTH SIDES
• If I have x something, Im done

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Another example

• 2x 12.4 32.4
• 12.4 12.4
• 2x 44.8
• 2 2
• x 22.4

• 12.4 is being subtracted from x, so we UNDO it by
  ADDING 12.4 to both sides
• We dont quite have x something so we have more
  work to do
• X is being multiplied by 2, so we UNDO it by
  DIVIDING both sides by 2
• X something, we are done!

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I can solve equations

• "You gotta do the same thing on both sides
• Examples
• p 8 14.1
• n 4.7 -4.7
• x -7
• 1.2
• n 3.9 0.7
• -6.3n -8.19
• 32.663 p 11.363

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Assignment

• P. 216- 217 9, 22, 23, 38, 40, 41