Section 7.3 - Solve Linear Equations

1
Section 7.3 - Solve Linear Equations

• Focus on
• solving and verifying simple linear equations
  algebraically

2
How do we solve equations?

• The basic idea of solving an equation is having
  an equation that is balanced on both sides.
  Picture a scale with the same values on each
  side.

3
Equations

• An equation is useful in finding the value of a
  missing number. Say we had an equation like this
• The empty box indicates a missing number. We know
  something should go there, but what?

4
You try this

• Look at two equations and find a number for x
  that makes the left side of the equation EQUAL to
  the right side.
• 3x 18 4x 60 80

5
Examples

• 4 5 9
• 4 5 7 9 7
• 16 16 this equation is still equal
• 4 5 9
• 4 5 3 9 3
• 6 6 this equation is still equal

6
Examples

• 4 5 9
• 2(4 5) 2(9)
• 18 18 this equation is still equal
• 4 5 9 this equation is still equal
• (4 5)/3 (9)/3
• 3 3

7
Steps to Solving Equations

• 1) Simplify both sides of the equation by using
  the distributive property and combining like
  terms, if possible.
• 2) Move all terms with variables to one side of
  the equation, and then simplify (ensure that your
  equations remains balanced at all times).
• 3) Move the constants to the other side of the
  equation and simplify (keeping your equation
  balanced).
• 4) If there is a coefficient in front of your
  variable, divide both sides by that number.

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Example

• 3x 7 13
• 3x 7 13
• Subtract 7 from both sides, we get
• 3x 7 - 7 13 - 7
• 3x 6
• Dividing both sides by 3, we get
• 3x 6
• 3 3
• x 2

9
You try these

• 3(x 4) 36
• 2(x 4) 16