What Are Linear Equations in One Variable?
Equations using a single variable with a maximum power of one are known as linear equations in one variable.
An example of a linear equation in one variable is x + 3 = 7.
It is named linear because it plots like a straight line on a graph!
🧠 Understanding the Basics
A linear equation in one variable generally looks like this:ax + b = c
Where:
xis the variablea,b, andcare constantsa ≠ 0
Goal: Find the value of x that makes both sides equal.
✏️ How to Solve Linear Equations – Step-by-Step
Let’s go through a simple example.
Example 1:x + 5 = 12
✅ Step 1: Move constants to one side:
Subtract 5 from both sides:x + 5 - 5 = 12 - 5x = 7
Example 2:2x - 3 = 9
✅ Step 1: Add 3 to both sides:2x - 3 + 3 = 9 + 32x = 12
✅ Step 2: Divide both sides by 2:x = 12 ÷ 2 = 6
🎉 Final Answer: x = 6
💡 Tips to Remember
- On both sides of the equation, always do the same procedure.
- On one side, try to isolate the variable (x).
- As with a weighing scale, keep equations balanced.
- Re-enter your response into the equation to verify it.
🎲 Real-Life Example
Imagine you bought a notebook and a pen for ₹80. If the pen costs ₹30, how much did the notebook cost?
Let notebook cost = x
Then, x + 30 = 80
Solving: x = 80 - 30 = ₹50
Yes, math helps you in shopping too! 😄
✨ Word Problems on Linear Equations
- A number increased by 9 gives 25. What is the number?
Let the number bex.
Equation:x + 9 = 25
Solution:x = 16 - Five times a number is equal to 60. Find the number.
5x = 60 → x = 12
🧩 Practice Time! (Try Solving These)
3x + 4 = 195x - 2 = 182x + 7 = x + 104(x - 2) = 2x + 6
✍️ (Need answers? Just ask!)
📊 Why Are Linear Equations Important?
- utilized in physics, business, algebra, and even coding
- aids in problem-solving and logical thinking
- serves as the foundation for more complex mathematical concepts like graphs and quadratic equations.
🧠 Fun Fact
The word “linear” comes from line. Every solution of a linear equation in one variable lies on a straight line in algebra!
📚 Conclusion
One-variable linear equations are difficulties having practical applications rather than only mathematical issues. Children start to love math more as they figure out how to balance and solve problems!
👉 Continue to practice. Start out easy. And eventually, it will be as simple as counting to solve 2x + 3 = 15.
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