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Algebraic Sense
Lesson 21		 Evaluation and Solving
  Objectives/Vocab/Tips > Examples 1 | 2 | 3 | 4 > Practice: 1 | 2 | 3 | 4 > Reflection

ALPObjective:

Evaluating and Solving

In this lesson you will evaluate expressions and formulas and solve single-variable equations.

Vocabulary:

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  • equation
  • expression
  • function
  • symbol
  • unknown
  • variable
Tips to Remember:

What You Do On One Side of the Equation . . .

When solving for variables with an equation, you will need to use different properties of numbers and different operations to end up with your final answer. Just remember, no matter what you do on one side of the equation or equal sign, you need to do the same thing on the other side. For example, if you need to add 7 to one side of the equation to help get your variable by itself, you can do that as long as you add 7 to the other side of the equal sign. Don't forget!

Solving Equations with One Variable

Operation
Rule
Example
Addition
 You can add the same number to both sides of an equation without changing the solution.

x - 4 = 5
x - 4 + 4 = 5 + 4
x = 9
Subtraction
 You can subtract the same number to both sides of an equation without changing the solution.
x + 3 = 11
x + 3 - 3 = 11 - 3
x = 8
Multiplication
 You can multiply both sides of an equation by the same nonzero number without changing the solution.
1/3x = 5
3 * 1/3x = 5 * 3
x = 15
Division
 You can divide both sides of an equation by the same nonzero number without changing the solution.
4x = 16
4x/4 = 16/4
x = 4

Solving Inequalities with One Variable

Operation
Example
Add the same number to both sides
x - 2 < 3
x - 2 + 2 < 3 + 2
x < 5
Subtract the same number from both sides
x + 3 < 5
x + 3 - 3 < 5 - 3
x < 2
Multiply both sides by a positive number
1/3x < 10
3 * 1/3x < 10 * 3
x < 30
Divide both sides by a positive number
2x < 10
2x/2 < 10/2
x < 5
Multiply both sides by a negative number
 Same as multiplying by a positive, except that the sign is reversed in direction.
Divide both sides by a negative number
 Same as dividing by a positive, except that the sign is reversed in direction.

 

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