Mathematics Linear Equation Class6
Introduction
Assalamualikum dear students, In this article, we will be exploring linear equations in mathematics. Linear equations are an essential part of algebra and are widely used in various problem-solving scenarios. We will go through the process of solving linear equations and understanding their equivalent forms but first I will tell you the book name where I give the solution to the question named Cambridge Scholar Standard Series Class 6 Mathematics.
You can watch the YouTube video to understand the Linear Equation clearly!
Solving the Equations
Let's start by solving a specific problem, identified as Question 3. The given equation is x - 4 - 9. To solve this equation, we need to simplify it using the rules of mathematics.
First, we will put -9 and x - 4 in separate round brackets for simplification. Then, we will multiply the outer bracket with the inner bracket using the distributive property. In this case, multiplying -9 with x - 4 will give us -9x + 36. Now, our equation becomes -9x + 36 = 0.
Next, we will simplify the equation further. We will bring the constants (36) to the right-hand side and the variable (-9x) to the left-hand side. Thus, the equation becomes -9x = -36.
Now, we will divide both sides of the equation by -9 to isolate the variable. Dividing -36 by -9 gives us x = 4.
Equivalent Equations
An equivalent equation is one that has the same solution as the original equation. Let's consider the equation x - 4 - 9 again. We have solved this equation and obtained the solution x = 4.
We can write equivalent equations by performing certain mathematical operations on the original equation. In this case, we will multiply both sides of the equation by 2. Multiplying -9x = -36 by 2 gives us -18x = -72.
Another equivalent equation can be obtained by multiplying both sides of the equation by 3. Multiplying -9x = -36 by 3 gives us -27x = -108.
It is important to note that these equivalent equations have different forms but yield the same solution (x = 4).
Importance of Sign
In mathematics, the sign before a number is crucial in determining the operation to be performed. When there is no sign present before a number, it is considered positive. However, if there are two consecutive signs (either plus or minus), they cancel each other out.
For example, in the equation -9x + 36 = 0, the minus sign before 9 cancels out with the minus sign before x, making it positive. Hence, we get 9x + 36 = 0.
Similarly, in the equation 3x - 12 - 27 = 0, the plus sign before 3 cancels out with the minus sign before 12, making it negative. Hence, we get 3x - 12 + 27 = 0.
Understanding the signs correctly is essential for solving linear equations accurately.
Conclusion
Linear equations are fundamental in mathematics and play a significant role in problem-solving. By following specific rules and simplifying the equations, we can arrive at the correct solutions. Equivalent equations allow us to manipulate the given equation without changing its solution. Paying attention to signs is crucial in correctly solving linear equations.