Solving Linear Equations

1
Solving Linear Equations

• Using Multiplication/Division

2
Solving 1-Step Equations

• To find the solution to an equation we must
  isolate the variable.
• We isolate the variable by performing operations
  that will eliminate (cancel) the other numbers
  from the expression.
• The Multiplication Property of Equality says that
  we can multiply the same number on both sides of
  an equation without changing the solution to the
  equation.

3
Multiplication Property of Equality

• Take the equation 3x 15
• Our goal is to multiply a number on both sides of
  the equation that will isolate the x by
  canceling the coefficient of x, 3.
• Since 3 and x are multiplied, we dont want to
  cancel 3 to a zero, we want to cancel 3 to a
  value of one. (Perform an operation that will
  make 3x become 1x x.)

4
Multiplication Property of Equality

• What number, when multiplied by 3, will give us
  one?

• The Multiplication Property of Equality says we
  can multiply 1/3 to the equation as long as we
  multiply it on both sides.

5
Multiplication Property of Equality

• See what happens

Multiply 1/3 on both sides of the equal sign.
6
Checking the Solution

• Always check the solution by substituting the
  value back into the original equation.

3x 15
3 5 15
15 15

• The sentence should be true.

7
Solving by Multiplication

• Multiply both sides of the equation by the number
  that will cancel with the coefficient of the
  variable. This will isolate the variable by
  making its coefficient the number 1.
• Reciprocals multiply to 1. The reciprocal of a
  whole number is 1 over the number.

8
Examples
Multiply 3/2 on both sides of the equal sign.
Check
9
Examples
Multiply 1/4 on both sides of the equal sign.
Check
10
Examples
w/5 is the same thing as 1/5 w, multiply both
sides by 5/1.
Check
11
Try These!
12
Solutions!
13
Solutions!