Answer:
Step-by-step explanation:
Sure! Let's imagine you're five, and we're going to talk about something fun and easy to understand: balancing scales with toys.
### Linear Equations in One Variable
**What is a Linear Equation?**
Think of a linear equation like a see-saw (a playground balance) with toys on both sides. You want to make sure both sides are balanced and have the same number of toys.
**One Variable**
The one variable is like a mystery box that we need to find out how many toys are inside. We call this box "x". Sometimes, it might be a "y" or another letter, but let's stick with "x" for now.
### Example:
Imagine you have a see-saw. On one side, you have a mystery box "x" and 3 more toys. On the other side, you have 5 toys. You want to figure out how many toys are in the mystery box to keep the see-saw balanced.
Here's what it looks like:
\[ x + 3 = 5 \]
This means:
- "x" (the mystery box) plus 3 toys equals 5 toys.
### Solving the Equation
To find out how many toys are in the mystery box, we need to keep the see-saw balanced while removing the extra toys from one side. We do this by:
1. **Removing 3 toys from both sides.**
So, you take away 3 toys from each side:
\[ x + 3 - 3 = 5 - 3 \]
This simplifies to:
\[ x = 2 \]
So, the mystery box "x" has 2 toys inside to make both sides balanced!
### More Examples:
#### Example 1:
\[ 2x = 8 \]
This means:
- Two mystery boxes with the same number of toys in each equals 8 toys altogether.
To find out how many toys are in each mystery box, divide 8 toys by 2 boxes:
\[ x = 8 \div 2 \]
\[ x = 4 \]
Each box has 4 toys.
#### Example 2:
\[ x - 4 = 6 \]
This means:
- The mystery box with 4 toys taken away equals 6 toys.
To find out how many toys are in the mystery box, add 4 toys back:
\[ x - 4 + 4 = 6 + 4 \]
\[ x = 10 \]
So, the mystery box "x" has 10 toys.
### Conclusion
Linear equations in one variable are like simple puzzles where we balance a see-saw by finding out how many toys (the variable) are in the mystery box. We use basic adding, subtracting, multiplying, or dividing to solve these puzzles and keep everything balanced.
