Solving linear equations involves isolating the variable (usually 'x') to find its value. We do this by performing the same operations on both sides of the equation to maintain balance. The goal is to get 'x' by itself on one side of the equals sign. Remember the order of operations (PEMDAS/BODMAS) in reverse when isolating the variable!
For example, in the equation $2x + 3 = 7$, we first subtract 3 from both sides: $2x = 4$. Then, we divide both sides by 2 to get $x = 2$. With practice, these steps become second nature.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Variable | a. A statement that two expressions are equal. |
| 2. Coefficient | b. A value that does not change. |
| 3. Constant | c. A symbol (usually a letter) representing an unknown value. |
| 4. Equation | d. The number multiplied by a variable in an algebraic expression. |
| 5. Solution | e. The value(s) that make an equation true. |
Complete the following paragraph with the correct terms:
To solve a linear equation, we want to ___________ the variable. This means getting the variable by ___________ on one side of the equation. We use inverse ___________ to undo operations and maintain ___________ by doing the same thing to both sides. The value of the variable that makes the equation true is called the ___________.
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.
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