๐ Topic Summary
Solving equations of the form $ax + b = c$ involves isolating the variable 'x' to find its value. This is achieved by using inverse operations to undo the operations performed on 'x'. The goal is to get 'x' by itself on one side of the equation. Remember, whatever operation you perform on one side of the equation, you must perform on the other side to maintain balance. For example, to solve $2x + 3 = 7$, you would first subtract 3 from both sides, then divide both sides by 2.
These equations are fundamental in algebra and are used to represent and solve various real-world problems. Mastering this skill is essential for more advanced mathematical concepts.
๐ง Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Variable |
A. A number on its own |
| 2. Coefficient |
B. A symbol representing an unknown value |
| 3. Constant |
C. A mathematical statement that two expressions are equal |
| 4. Equation |
D. A number multiplied by a variable |
| 5. Inverse Operation |
E. An operation that undoes another operation |
Match the following:
- ๐ Variable = B
- ๐ก Coefficient = D
- ๐ Constant = A
- ๐ Equation = C
- ๐งฎ Inverse Operation = E
โ๏ธ Part B: Fill in the Blanks
Fill in the blanks with the correct words:
To solve an equation like $ax + b = c$, we need to ________ the variable. First, we use the ________ operation to remove the ________. Then, we ________ both sides by the ________ to find the value of x.
Possible Answers:
- ๐ isolate
- โ inverse
- โ constant
- โ divide
- โ๏ธ coefficient
๐ค Part C: Critical Thinking
Explain in your own words why it's important to perform the same operation on both sides of an equation when solving for a variable.