Learning Objectives
Introduction
Tutorial
Two expressions set equal to each other.
An equation that can be written in the form
ax + b = c
where a, b, and c are constants.
3x - 4 = 5
A value, such that, when you replace the variable with
it,
it makes
the equation true.
(the left side comes out equal to the right side)
Set of all solutions
Get the variable you are solving for alone on one side and everything else on the other side using INVERSE operations.
If a = b, then a + c = b + c
If a = b, then a - c = b - c
Note that addition and subtraction are inverse operations of each other. For example, if you have a number that is being added that you need to move to the other side of the equation, then you would subtract it from both sides of that equation.
*LCD = 4
*1/2 = 2/4
At this point we are limited. We only have talked about using the addition and subtraction properties of equality. In Tutorial 13, we will address the multiplication and division properties of equality. But since this was made before that, we have to make ado with addition and subtraction.
We can solve this with what we know so far. We move a term that has a variable exactly the same way we were moving constants in examples 1 and 2. In this problem we need to get a on one side and everything else on the other. We have a -.7a on the right side. To move it to the other side, so a is only on one side, we will do the inverse of minus, which is add .7a to both sides.
After that it looks like examples 1 and 2 above, and we continue doing inverse operations until we have a on one side and everything on the other side of the equation.
Let's see what we get:
*Inverse of add 1.2 is sub. 1.2
Using the distributive property and then combining like terms to simplify the left side of the equation we get:
*Inverse of sub. 14 is add. 14
We can use that concept to figure out our problem. Anytime you know the total of two numbers, you subtract the given from the total to either find the other number or express the other number in terms of a variable.
Since our total is 100 and we are letting x represent one number, the other number would be expressed as the total minus x or 100 - x.
So, 100 - x is our answer.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1d: Solve the given equation.
Practice Problem 2a: Write an algebraic expression.
Need Extra Help on these Topics?
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 26, 2011 by Kim Seward.
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