4 Algebra

What is Algebra?

Algebra is the branch of mathematics which uses symbols (also known as variables) to represent numbers which do not have a known amount. Letters are often used as the symbols for variables to represent values which are unknown in an equation. To determine the actual value of the variable(s) is called “solving the equation”. Practicing how to solve for variables can support the development of your ability to calculate medication dosages safely as the preparation of medication often requires you to solve for an unknown amount.

Solving Equations

It is important to note the total value on each side of the equals sign is the same. You may recall that before solving an equation you may need to simplify it by combining all like terms together and then solving for the unknown variable(s). The majority of problems you must solve in medication administration will only require you to use basic math skills (adding, subtracting, multiplying and/or dividing) with real numbers and fractions.

Points to remember:

• Each side of the equation is equal.
• Simplify the problem by combining all like terms together.
• Use order of operations when solving the equation.
• If you do something to one side of the equation to simplify, you must do it to the other in order to keep both sides of the equation equal.

Solve the following equation:

[latex]2x + 4 = 12[/latex]

First, let’s get all the like terms together. Terms in this equation are 2x, 4 and 12. 4 and 12 are like terms because they are whole numbers. 2x does not have another like term. To get 4 and 12 together, we need to do something to both sides of the equation to cancel the 4 on the left side and bring it to the right side of the equals symbol.

[latex]2x + {4 - 4} = {12 - 4}[/latex]
[latex]2x = 8[/latex]

Now get x by itself. To do this we must cancel out the 2, which we can do if we divide both sides by 2.

[latex]\dfrac{{2}x}{{2}} =\dfrac{8}{2}[/latex]
[latex]x=4[/latex]

*In a shortened form of this process, this means when joining like terms that are being added or subtracted, you can just move the term across the equals sign and do the opposite function. Similarly, when moving terms that are being multiplied or divided, you can do the opposite function if it crosses the equals sign.

Practice

In the next section, you can practice solving randomly generated equations. You may want to have something to write on as you are solving these questions. You can practice questions with and without a calculator.

If you would like to review algebra in more detail, refer to Introductory Algebra by Izabela Mazur.^[1]

Practice Set 4.1: Solving Equations

Included in this chapter are two quizzes to practice basic algebra equations (more precisely, linear equations).

• Start with the first quiz which includes equations with only whole numbers.
• For an additional challenge, try without a calculator! Although calculators are often available to assist with tasks requiring arithmetic in the workplace, practice without a calculator is also beneficial. It is a great exercise for your brain health and you may find your speed of mental calculations improving with repeated practice.

The second quiz is extra challenging, with the addition of fractions in most questions. Practicing these questions will help you consolidate your understanding of how to simplify, add, subtract, multiply and divide fractions. You will not need to be proficient in these questions to be able to understand most numerical information found in the field of nursing.

Quiz Instructions

• Click the start button to generate quiz questions.
• The quiz will count down and then begin to provide randomly generated questions.
• Each quiz will generate ten multiple choice questions each time you click the start button.
• You will be able to view one question at a time.
• When ready, click on the answer you think is correct.
• If it is the correct answer, the box changes to green and you will hear a sound indicating a correct answer.
• If it is not the correct answer, the box you click changes to a darker shade of blue and the correct answer is highlighted in green.
• You can track self improvement by the number of correctly answered questions and/or by the amount of time you take to complete the quiz.

Quiz #1

Quiz #2