Pre-Algebra Unit 6 — One-Step Equations.
This unit covers addition equations, subtraction equations, multiplication equations and division equations — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers addition equations, subtraction equations, multiplication equations and division equations — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Addition Equations
An addition equation has a variable being added to a number. To solve, subtract the same number from both sides to isolate the variable. Always check your answer by substituting it back into the original equation.
Key Points
- Inverse operation of addition is subtraction
- Whatever you do to one side, you must do to the other
- The goal is to get the variable alone on one side
- Answer can be positive, negative, or zero
Solve: x + 7 = 15
Subtract 7 from both sides: x + 7 - 7 = 15 - 7, which gives x = 8. Check by substituting: 8 + 7 = 15, which is true.
2 Subtraction Equations
A subtraction equation has a number being subtracted from a variable. To solve, add the same number to both sides to isolate the variable. Be careful when the equation is written as a number minus a variable, as this requires an extra step.
Key Points
- Inverse operation of subtraction is addition
- Add the subtracted value to both sides to cancel it out
- Watch for negative results — the answer may be a negative number
- Always verify your solution in the original equation
Solve: x - 9 = 4
Add 9 to both sides: x - 9 + 9 = 4 + 9, which gives x = 13. Check: 13 - 9 = 4, which is true.
3 Multiplication Equations
A multiplication equation has the variable being multiplied by a coefficient. To solve, divide both sides by that coefficient to isolate the variable. This applies even when the coefficient is a fraction or negative number.
Key Points
- Inverse operation of multiplication is division
- Divide both sides by the coefficient of the variable
- If the coefficient is negative, dividing flips the sign of the answer
- A coefficient of 1 means the variable is already isolated
Solve: 6x = 42
Divide both sides by 6: 6x ÷ 6 = 42 ÷ 6, which gives x = 7. Check: 6(7) = 42, which is true.
4 Division Equations
A division equation has the variable being divided by a number. To solve, multiply both sides by that divisor to isolate the variable. The variable must be in the numerator for this method to work directly.
Key Points
- Inverse operation of division is multiplication
- Multiply both sides by the number in the denominator
- The result may be larger than numbers in the original equation
- Always simplify your answer fully before checking
Solve: x ÷ 5 = 9
Multiply both sides by 5: (x ÷ 5) × 5 = 9 × 5, which gives x = 45. Check: 45 ÷ 5 = 9, which is true.
Questions, answered.
What is One-Step Equations?
One-Step Equations is Unit 6 of Pre-Algebra, covering addition equations, subtraction equations, multiplication equations and division equations.
How to study for Pre-Algebra Unit 6?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.