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# Algebra for Nursing School Entrance Exam Study Guide

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Updated on Aug 12, 2011

The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems

Popular topics for algebra questions on nursing school exams 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.

### Operations

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:

### Equations

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 previous complicated equation. We want to solve for n, which means 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.

Notice that each operation in the original equation was undone by using its 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:

### Positive and Negative Numbers

Positive and negative numbers, also known as signed numbers, are best shown as points along the number line:

Numbers to the left of (smaller than) 0 are negative and those to the right are positive. Zero is neither negative nor positive. If a number is written without a sign, it is assumed to be positive. Notice that when you are on the negative side of the number line, bigger numbers have smaller values. For example, –5 is less than –2.You come into contact with negative numbers more often than you might think; for example, very cold temperatures are recorded as negative numbers.

As you move to the right along the number line, the numbers get larger. Mathematically, to indicate that one number, say 4, is greater than another number, say –2, the greater than sign (>) is used:

4 > –2

On the other hand, to say that –2 is less than 4, we use the less than sign (<):

–2 < 4