6.1 Solving Equations

Focus: solve equations by inspection and by systematic trial

Equation: a mathematical statement that two expressions are equal.

What is the difference between an Equation and an Expression?

Explore: (p-220) Solve this problem any way you like:



Method #1 - Inspection
Inspection - find the value of the variable using addition, subtraction, multiplication and division.

Ex: 2y + 5 = 11

First, Find a number that can be added to 5 to get 11.

6 + 5 = 11
so, 2y, must be equal to 6.

Then, we must find a number that, when multiplied by 2, is equal to 6.

3 x 2 = 6, so y = 3


Method #2 - Systematic Trial

Systematic Trial - choose a value for the variable, then check
by substitution. Use the answer and reasoning to choose the
next value you will try and check. (Fancy name for "Guess + Check.")

Ex: 3d - 4 = 14


Use equations to solve word problems:

Connect p. 20

Every equation needs a numerical coefficient, variable, a constant term, and a total which balances the equation. (The answer!)
Which piece of information is which?

NC:

v:

CT:

Total:

So, the Equation to solve is:



Practice: pg. 223 - 225 #1-10