Overview
This lecture explains how to solve one-step subtraction equations involving negative numbers by isolating the variable using inverse operations.
Solving One-Step Subtraction Equations with Negatives
- To isolate the variable, use the inverse (opposite) operation of what is being done to the variable.
- The inverse of subtraction is addition.
- Whatever you do to one side of the equation, you must do to the other side to keep the equation balanced.
Example 1: Solving J - 14 = -10
- To undo subtracting 14, add 14 to both sides: J - 14 + 14 = -10 + 14.
- The -14 and +14 cancel, leaving J = 4.
- Check by substituting: 4 - 14 = -10, which confirms the solution.
Example 2: Solving 18 = G - (-3)
- To undo subtracting -3, add -3 to both sides: 18 + (-3) = G - (-3) + (-3).
- Subtracting a negative is the same as adding a positive.
- G - (-3) can be rewritten as G + 3.
- To isolate G, subtract 3 from both sides: 18 - 3 = G.
- G = 15.
- Check by substituting: 18 = 15 - (-3); 15 - (-3) = 18, confirming the answer.
Working with Negatives and Showing Work
- Subtracting a negative increases the value (same as adding a positive).
- You may solve vertically or horizontally, depending on preference.
- Always check solutions by substituting the value back into the original equation.
Key Terms & Definitions
- Isolate the variable — Get the variable alone on one side of the equation.
- Inverse operation — The opposite mathematical operation (e.g., addition is the inverse of subtraction).
- Subtracting a negative — Equivalent to adding a positive number.
Action Items / Next Steps
- Practice solving one-step subtraction equations with positive and negative numbers.
- Check all solutions by substituting back into the original equation.