Solving Equations Using Multiplication and Division

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Solving Equations Using Multiplication and
Division
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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Remember, 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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Multiplication Property of Equality

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

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

• Would you ever put deodorant under just one arm?
• Would you ever put nail polish on just one hand?
• Would you ever wear just one sock?

• We all know that 3 3.
• Does 3(4) 3? NO!
• But 3(4) 3(4).
• The equation is still true if we multiply both
  sides by 4.

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Lets try another example!

• Always check your solution!!
• The original problem is
• x 4
• 2
• Using the solution x 8,
• Is x/2 4?
• YES! 4 4 and our solution is correct.

• x 4
• 2
• Multiply each side by 2.
• (2)x 4(2)
• 2
• x 8

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What do we do with negative fractions?

• The two negatives will cancel each other out.
• The two fives will cancel each other out.
• (-5) (-5)
• x -15
• Does -(-15)/5 3?

Recall that
Solve . Multiply both sides by
-5.
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Division Property of Equality

• For any numbers a, b, and c (c ? 0), if a b,
  then a/c b/c

What it means

• You can divide BOTH sides of an equation by any
  number - except zero- and the equation will still
  hold true.
• Why did we add c ? 0?

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2 Examples

• 1) 4x 24
• Divide both sides by 4.
• 4x 24
• 4 4
• x 6
• Does 4(6) 24? YES!

• 2) -6x 18
• Divide both sides by -6.
• -6y 18
• -6 -6
• y -3
• Does -6(-3) 18? YES!

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A fraction times a variable

• The two step method
• Ex 2x 4
• 3
• 1. Multiply by 3.
• (3)2x 4(3)
• 3
• 2x 12
• 2. Divide by 2.
• 2x 12
• 2 2
• x 6

• The one step method
• Ex 2x 4
• 3
• 1. Multiply by the RECIPROCAL.
• (3)2x 4(3)
• (2) 3 (2)
• x 6

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