Key Takeaways
- Solve equations by performing inverse operations to isolate the variable
- Combine like terms (same variable and exponent) before solving
- Translate words carefully: "less than" means subtraction, "more than" means addition
- When solving inequalities, reverse the sign when multiplying/dividing by a negative
- Always check your answer by substituting back into the original equation
Algebra and Equations
The TEAS tests basic algebraic skills including solving equations, working with variables, and translating word problems into mathematical expressions.
Algebraic Expressions
An expression contains numbers, variables, and operations but no equal sign.
Terms: Parts of an expression separated by + or - Coefficient: The number multiplied by a variable Constant: A number without a variable
| Expression | Terms | Coefficients | Constants |
|---|---|---|---|
| 3x + 5 | 3x, 5 | 3 | 5 |
| 2x² - 4x + 7 | 2x², -4x, 7 | 2, -4 | 7 |
Combining Like Terms
Like terms have the same variable raised to the same power.
Example: Simplify 3x + 5x - 2x
- All terms have variable x
- 3 + 5 - 2 = 6
- Answer: 6x
Example: Simplify 4x² + 3x - 2x² + 5x
- Combine x² terms: 4x² - 2x² = 2x²
- Combine x terms: 3x + 5x = 8x
- Answer: 2x² + 8x
Solving One-Step Equations
Goal: Isolate the variable by performing inverse operations.
| If the equation has... | Do this... | Example |
|---|---|---|
| Addition | Subtract | x + 5 = 12 → x = 7 |
| Subtraction | Add | x - 3 = 10 → x = 13 |
| Multiplication | Divide | 4x = 20 → x = 5 |
| Division | Multiply | x/3 = 6 → x = 18 |
Solving Two-Step Equations
Order: Undo addition/subtraction first, then multiplication/division.
Example: Solve 3x + 7 = 22
- Subtract 7: 3x = 15
- Divide by 3: x = 5
Example: Solve (x/4) - 3 = 5
- Add 3: x/4 = 8
- Multiply by 4: x = 32
Solving Multi-Step Equations
Steps:
- Distribute if needed
- Combine like terms on each side
- Move variables to one side
- Move constants to the other side
- Isolate the variable
Example: Solve 2(x + 3) = 4x - 6
- Distribute: 2x + 6 = 4x - 6
- Subtract 2x: 6 = 2x - 6
- Add 6: 12 = 2x
- Divide: x = 6
Translating Words to Algebra
| Words | Operation | Example |
|---|---|---|
| Sum, plus, more than, increased by | + | x + 5 |
| Difference, less than, decreased by | - | x - 3 |
| Product, times, of | × | 3x |
| Quotient, divided by, per | ÷ | x/4 |
| Is, equals, is the same as | = | x = 10 |
| Twice, double | × 2 | 2x |
| Half | ÷ 2 | x/2 |
Setting Up Word Problems
Example: "Five more than twice a number is 17. Find the number."
- Let x = the number
- Twice a number: 2x
- Five more than: 2x + 5
- Is 17: 2x + 5 = 17
- Solve: 2x = 12, x = 6
Inequalities
Symbols:
- < less than
-
greater than
- ≤ less than or equal to
- ≥ greater than or equal to
Solving: Same as equations, but reverse the inequality when multiplying or dividing by a negative number.
Example: Solve -2x < 6
- Divide by -2 (reverse sign): x > -3
Healthcare Algebra Applications
| Scenario | Equation |
|---|---|
| BMI calculation | BMI = weight(kg) / height(m)² |
| IV flow rate | Rate = Volume / Time |
| Dosage | Dose = Weight × mg/kg |
| Dilution | C₁V₁ = C₂V₂ |
Solve for x: 4x - 7 = 21
Simplify: 5x² + 3x - 2x² + 7x - 4
"Three less than four times a number equals 17." Which equation represents this?