284 Essential Skills for Health Careers Success
division—to isolate the unknown on one side of the equation. This will
help you determine the value of the unknown.
Example: 3x - 5 = 10
3x – 5 = 10
+5 +5
Add 5 to both sides of the equation to isolate the 3x on the left.
3x = 15
3 3
Divide each side by 3, so that only the x remains on the left-hand side
of the equation.
x = 5
To check your answer, plug 5 into the equation where x appears.
3(5) – 5 = 10
15 – 5 = 10
10 = 10
Because both sides of the equation are equal, you know that 5 is the
correct answer.
One way algebra is commonly used in healthcare is to calculate medi-
cine dosage. Nurses, in particular, are responsible for performing these cal-
culations and administering the proper amount of medicine to a patient.
The following example shows one way of using algebra to calculate the
ml (milliliters) amount for a liquid medication administered by injection
(Figure 10.9).
To calculate the amount of medicine to administer, use the following
algebraic equation:
D (desired dose)
× V (vehicle) = x (amount to be administered)
H (have on hand)
Example: A vial of medication states that there are 300 mg of the
medicine per 0.5 ml. The doctor orders 600 mg of medication to
be administered to the patient. How many ml of the medication
should the nurse inject?
600 mg
× 0.5 = x
300 mg
600/300 = 2
2 × 0.5 = x
x = 1 ml
The nurse should administer one ml of the medicine to achieve
the desired dose of 600 mg.
Kidsana Maimeetook/Shutterstock.com
Figure 10.9 Calibrated
syringes are used for medica-
tion injections.