📚 Topic Summary
Imagine you have a secret number, which we call $x$. Someone takes away a certain amount ($a$) from your secret number, and you end up with a new number ($b$). Solving equations like $x - a = b$ means finding out what that original secret number ($x$) was. To do this, we simply add the amount that was taken away ($a$) back to the final number ($b$). The formula is: $x = a + b$
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Variable |
A. The answer to an equation |
| 2. Equation |
B. A mathematical statement that two expressions are equal |
| 3. Solution |
C. Adding the opposite to both sides of the equation. |
| 4. Inverse Operation |
D. A symbol (usually a letter) that represents an unknown number |
| 5. Constant |
E. A number that does not change its value. |
Answer Key: 1-D, 2-B, 3-A, 4-C, 5-E
✍️ Part B: Fill in the Blanks
To solve the equation $x - 5 = 12$, we need to isolate the $x$. We do this by performing the ___________ operation, which is adding 5 to both sides of the _________. This gives us $x = 12 + 5$, so $x = $ ___________. Therefore, the value of $x$ is __________.
Answer Key: inverse, equation, 17, 17
🤔 Part C: Critical Thinking
Explain in your own words why adding the same number to both sides of an equation keeps the equation balanced.
