TEAS Algebra Practice Questions With Step-by-Step Solutions

The algebra questions in the TEAS exam fall under the numbers and algebra domain. It focuses on skills such as one-variable equations, inequalities, and translating word problems into expressions. All of these questions follow clear steps, so they can become easier to solve when you work through TEAS algebra practice questions. In this article, we will provide TEAS algebra step-by-step solutions for some of the common question types instead of only giving you an answer key. Each solution explains how to approach the problem and choose the right method to reach the correct answer with confidence.

What Counts as “Algebra” on the TEAS

We will focus on the algebra-specific skills in this article and not the fraction, decimal, and other arithmetic questions. There are 38 scored mathematics questions in the TEAS exam, and 16 of these questions are on numbers and algebra.

Algebra-specific skills can be broken down into four recurring categories:

• Solving one-variable linear equations
• Solving and interpreting one-variable inequalities, including the negative-number sign-flip rule
• Translating written phrases and word problems into expressions, equations, or inequalities
• Solving proportions using cross-multiplication

If you would like to practice other mathematics skills, you can go through our TEAS fractions and decimals practice questions separately.

Worked Example 1 — One-Variable Equation

TEAS one-variable equations practice usually follows a simple two-step pattern. First, you need to undo addition or subtraction. Then, you have to undo multiplication or division to isolate the variable and get the answer.

Problem: Solve for x:
4x + 7 = 23

Step 1: Subtract 7 from both sides.
4x = 16

Step 2: Divide both sides by 4.
x = 4

Answer:x = 4

Worked Example 2 — Inequality With a Negative Coefficient

TEAS inequality practice questions follow the same basic solution as other equations. First, you need to remove the number added to the variable. Then, divide by the coefficient. If you divide by a negative number, then remember to reverse the inequality sign. Forgetting to do this is one of the most common TEAS algebra mistakes.

Problem: Solve for x:
-3x + 5 > 20

Step 1: Subtract 5 from both sides.
-3x > 15

Step 2: Divide both sides by -3.
x < -5

Why did the sign change? Dividing by a negative number reverses the inequality sign from > to <.

Remember: When you multiply or divide both sides of an inequality by a negative number, always reverse the inequality sign.

Answer:x < -5

Worked Example 3 — Translating a Word Problem Into an Equation

TEAS word problems often require you to turn words into an equation before solving it. Look for phrases such as “twice” and “3 more than” to identify the correct operations.

Problem: A nurse has 3 more than twice the number of patients as her colleague. If she has 17 patients, how many does her colleague have?

Step 1 (Translate): Let x = the colleague’s patients. “Twice the number” = 2x, and “3 more than” means + 3, so the equation is 2x + 3 = 17

Step 2 (Solve): Subtract 3 from both sides → 2x = 14; divide both sides by 2 → x = 7

Answer: 7 patients

In these questions, translation is a separate step. When you translate word problems into equations on the TEAS, setting up the equation correctly is often the hardest part. Writing the equation correctly helps you avoid mistakes and solve it easily.

Worked Example 4 — Proportion (Dosage-Style Word Problem)

TEAS proportion word problems often use real-world situations where two quantities have the same relationship. These dosage-style questions are useful for nursing students because they practice setting up and solving proportions.

Problem: If 5 mL of medication contains 250 mg, how many mL are needed for a 400 mg dose?

Step 1 (Set up the proportion):
5/250 = x/400

Step 2 (Cross-multiply):
250x = 5 × 400
250x = 2000

Step 3 (Solve):
x = 2000 ÷ 250
x = 8

Answer:8 mL

Proportions are useful in nursing because medication calculations often require matching a certain amount of medication to a prescribed dose. Practicing these problems helps applicants build necessary skills of comparing quantities, setting up relationships correctly, and solving dosage calculations. This is why proportion-based questions are important to practice.

Worked Example 5 — Multi-Step Word Problem With an Inequality

TEAS inequality word problems can have several steps.

Problem: A clinic has a supply budget of $180. Each box of gloves costs $12, and the clinic has already spent $60 on other supplies. What is the maximum number of glove boxes the clinic can buy?

Step 1 (Translate): Let x = the number of glove boxes. Total spend = 12x + 60, which must stay at or under $180 → 12x + 60 ≤ 180

Step 2 (Solve): Subtract 60 from both sides → 12x ≤ 120

Step 3 (Solve): Divide both sides by 12 → x ≤ 10

Answer: A maximum of 10 boxes

In this question, a sign flip is not needed as both sides were divided by a positive number.

Common Algebra Mistakes on the TEAS (And How These Examples Avoid Them)

All of the above examples were built around the most common errors that TEAS candidates make.

• Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
• In a word problem, students can make the mistake of translating the equation wrong and solving the question for the wrong variable.
• Skipping the translation step and guessing an equation from the word problem, which can cause setup errors.
• Rounding numbers too early in a multi-step proportion problem, which can affect the final answer.

If you know the questions well but still struggle to complete them quickly, you should read the TEAS math section: how to solve problems quickly without a calculator. This covers pacing tips that will help you with solving the questions quickly.

Frequently Asked Questions

What algebra topics are on the TEAS math section?

The TEAS covers several algebra questions such as one-variable linear equations, one-variable inequalities, translating word problems into expressions or equations, and proportions solved by cross-multiplication.

How do you solve a one-variable equation on the TEAS?

To solve the one-variable equation, you need to isolate the variable by doing the same operation on both sides. Work one step at a time. For example, subtract the constant first, then divide by the number next to the variable to find its value.

What’s the rule for inequalities with negative numbers on the TEAS?

When solving inequalities with negative numbers, you need to reverse the direction of the inequality sign. Most of the candidates make this common mistake that leads to incorrect answers.

Why are proportions important for nursing students on the TEAS?

Proportions are important because they help nursing students develop the skill of dosage calculations. These questions are based on cross-multiplication and compare two quantities. This is why the TEAS exam weights these proportion-based questions heavily within its algebra content.

Can I use a calculator for TEAS algebra questions?

It depends on the specific question you are solving. For some questions, an on-screen four-function calculator is allowed, while other questions are calculator-restricted, and you need to solve them step-by-step.

Conclusion

The TEAS algebra questions are based on formulas, and they can be easily learned when candidates understand the underlying steps. You can use TEAS algebra practice questions to understand the patterns and rules. You can also follow the guide on how to guess smartly on TEAS questions without losing marks if you get confused. We provide TEAS exam tutoring services and an online TEAS practice test so you can prepare confidently. You can contact us if you require more details.