Algebra Review for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide
Algebra questions do not appear on every test. However, when they do, they typically cover the material you learned in pre-algebra or in the first few months of your high school algebra course. Popular topics for algebra questions include:
- solving equations
- positive and negative numbers
- algebraic expressions
What Is Algebra?
Algebra is a way to express and solve problems using numbers and symbols. These symbols, called unknowns or variables, are letters of the alphabet that are used to represent numbers.
For example, let's say you are asked to find out what number, when added to 3, gives you a total of 5. Using algebra, you could express the problem as x + 3 = 5. The variable x represents the number you are trying to find.
Here's another example, but this one uses only variables. To find the distance traveled, multiply the rate of travel (speed) by the amount of time traveled: d = r × t. The variable d stands for distance, r stands for rate, and t stands for time.
In algebra, the variables may take on different values. In other words, they vary, and that's why they're called variables.
Algebra uses the same operations as arithmetic: addition, subtraction, multiplication, and division. In arithmetic, we might say 3 + 4 = 7, while in algebra we would talk about two numbers whose values we don't know that add up to 7, or x + y = 7. Here's how each operation translates to algebra:
An equation is a mathematical sentence stating that two quantities are equal. For example:
2x = 10
x + 5 = 8
The idea is to find a replacement for the unknown that will make the sentence true. That's called solving the equation. Thus, in the first example, x = 5 because 2 × 5 = 10. In the second example, x = 3 because 3 + 5 = 8.
Sometimes you can solve an equation by inspection, as with the above examples. Other equations may be more complicated and require a step-by-step solution, for example:
The general approach is to consider an equation like a balance scale, with both sides equally balanced. Essentially, whatever you do to one side, you must also do to the other side to maintain the balance. Thus, if you were to add 2 to the left side, you would also have to add 2 to the right side.
Let's apply this balance concept to our complicated equation above. Remembering that we want to solve it for n, we must somehow rearrange it so the n is isolated on one side of the equation. Its value will then be on the other side. Looking at the equation, you can see that n has been increased by 2 and then divided by 4 and ultimately added to 1. Therefore, we will undo these operations to isolate n.
- Begin by subtracting 1 from both sides of the equation:
- Next, multiply both sides by 4:
- Finally, subtract 2 from both sides:
- Which isolates n and solves the equation: n = 6.
Notice that each operation in the original equation was undone by using the inverse operation. That is, addition was undone by subtraction, and division was undone by multiplication. In general, each operation can be undone by its inverse.
After you solve an equation, check your work by plugging the answer back into the original equation to make sure it balances. Let's see what happens when we plug 6 in for n:
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