What are LHS and RHS in an Equation with Solved Examples
A linear equation is present in the forms of one-variable, two, or three-variable. In one variable, a linear equation, the standard equation looks like \[ax + b = 0\] where a and b are the constant numbers, and the x is the variable part we need to find. Similarly, the two-variable equation would look like \[ax + by + c = 0\] where a, b, and c are the constant and x and y are the variables. An example of a linear equation will be \[6 + x = 13\].
How to Solve Linear Equations?
To solve the linear equation with one variable method like LHS=RHS is used. In this method, the variable part and the constant part of the equation are separated from each other so that the value of the variable part can be found. The value is then put into the initial equation to check whether the correct value was found.
To solve the linear equation with two variables, methods like
Substitution method
Elimination method
Cross multiplication method, and
Plotting the graph method.
How to Find LHS and RHS?
Every algebraic equation has two sides: Right Hand Side (RHS) and Left Hand Side (LHS). In the case of an equation, the two sides are equal, that is, the left and right sides are equal. Let’s understand this using the LHS and RHS example.
\[2x + 5 = 15\] in this equation we have \[2x + 5\] on our LHS and 15 on our RHS. To prove that LHS is equal to RHS we need to find the value of the x.
For that, we will first assume that LHS and RHS are equal and will transfer the constant part of the equation to the RHS and solve it.
\[\begin{array}{l}2x + 5 = 15\\2x = 15 - 5\\x = \dfrac{{10}}{2}\\x = 5\end{array}\]
Now, we will put the value of x as 5 in our initial equation.
So, LHS= \[\begin{array}{l}2x + 5\\2(5) + 5\\10 + 5\\15\end{array}\]
As we got 15 on the LHS and it was given that RHS is also 15. Now we can say that LHS is equal to RHS.
Examples of Solving Linear Equations
Now, let’s work on some examples to understand how to solve linear equations with one variable.
To prove the given equation LHS is equal to RHS \[10x + 7 = 13 - 5x\].
Step one: assume LHS is equal to RHS.
Step two: Place the constant on RHS and the variable on the LHS.
Step three: Solve and find the value of the variable
Step four: Put this value first in the initial equation on LHS and then on RHS. If both sides have the same answer, then LHS would be equal to RHS.
Ans: Assuming LHS is equal to RHS.
\[\begin{array}{l}10x + 7 = 13 - 5x\\10x + 5x = 13 - 7\\15x = 6\\x = \dfrac{6}{{15}}\\x = \dfrac{2}{5}\end{array}\]
Putting the value of x on the LHS.
\[\begin{array}{l}10x + 7\\10(\dfrac{2}{5}) + 7\\4 + 7\\11\end{array}\]
Putting the value of x on the RHS.
\[\begin{array}{l}13 - 5x\\13 - 5(\dfrac{2}{5})\\13 - 2\\11\end{array}\]
As the value of LHS and RHS is 11 so; we can say that LHS is equal to RHS.
Conclusion
Linear equations can be present in one, two, or three-variable forms. The method to solve one variable equation is by finding out the value of the variable. Then putting it in the initial equation to check whether LHS is equal to RHS. If LHS is not equal to RHS, then the value of the variable you found is incorrect, or the equation does not have a value that would equate them.
Sample Questions
1. What is LHS?
a. Left Hour Sign
b. Left Hand Side
c. Less Hour Side
d. Left Home Sweet
Ans: Left Hand Side
2. Does LHS always equal RHS?
a. Yes
b. No
Ans: Yes
Explanation: LHS is always equal to RHS if the value of the variable we found out is right and there is no exception in the equation.
3. When the RHS and LHS are not equal then that equation is called
a. linear equality
b. linear inequality
c. Algebraic equality
d. Algebraic inequality
Ans: Linear Inequality
Explanation: When RHS and LHS are not equal to each other then the equation would have no solution or would have infinite solutions. Such equations are known as linear inequality equations.
FAQs on LHS and RHS in Maths with Clear Examples
1. What is LHS and RHS in Maths?
The LHS (Left-Hand Side) is the expression on the left of the equals sign (=), and the RHS (Right-Hand Side) is the expression on the right of the equals sign in an equation. In any mathematical equation, both sides are equal in value.
- Example: In 3 + 5 = 8
- LHS = 3 + 5
- RHS = 8
- Since both sides equal 8, the equation is true.
2. What is an example of LHS and RHS in an equation?
An example of LHS and RHS is 2x + 3 = 11, where 2x + 3 is the LHS and 11 is the RHS. To check equality:
- Step 1: Solve 2x + 3 = 11
- Step 2: Subtract 3 → 2x = 8
- Step 3: Divide by 2 → x = 4
- Step 4: Substitute x = 4
- LHS = 2(4) + 3 = 11
- RHS = 11
3. How do you solve an equation using LHS and RHS?
To solve an equation using LHS and RHS, simplify both sides and make the variable stand alone on one side. Follow these steps:
- Simplify LHS and RHS separately.
- Move like terms to one side.
- Isolate the variable.
- Verify by substituting the value back into both sides.
- Subtract 3x → 2x − 2 = 6
- Add 2 → 2x = 8
- Divide by 2 → x = 4
4. How do you check if LHS is equal to RHS?
To check if LHS = RHS, substitute the given value into both sides and compare the results. If both sides give the same number, the equation is true.
- Example: Check if x = 3 satisfies 2x + 1 = 7
- LHS = 2(3) + 1 = 7
- RHS = 7
- Since LHS = RHS = 7, the equation is verified.
5. What is the difference between LHS and RHS?
The difference between LHS and RHS is their position relative to the equals sign in an equation.
- LHS is the expression on the left side of =
- RHS is the expression on the right side of =
- Both sides must have equal values for a true equation
6. What does it mean if LHS is not equal to RHS?
If LHS ≠ RHS, the equation is false for the given value. This means the substitution or solution is incorrect.
- Example: Check x = 2 in 3x + 1 = 10
- LHS = 3(2) + 1 = 7
- RHS = 10
- Since 7 ≠ 10, the equation is not satisfied.
7. Can LHS and RHS contain algebraic expressions?
Yes, both LHS and RHS can contain algebraic expressions with variables, constants, and operations. For example:
- Equation: 3x + 5 = 2x + 9
- LHS = 3x + 5
- RHS = 2x + 9
8. What is an example of verifying LHS and RHS in identities?
To verify an identity, simplify LHS and show it equals RHS without substituting values. Example: Verify (a + b)² = a² + 2ab + b²
- LHS = (a + b)(a + b)
- = a² + ab + ab + b²
- = a² + 2ab + b²
- This equals RHS.
9. Why must LHS be equal to RHS in an equation?
In any equation, LHS must equal RHS because an equation represents equality between two expressions. If both sides are not equal, the statement is not mathematically true.
- Example: 8 − 3 = 5 is true because both sides equal 5.
- If 8 − 3 = 6, it is false because 5 ≠ 6.
10. What are common mistakes when comparing LHS and RHS?
Common mistakes when comparing LHS and RHS include calculation errors and not simplifying both sides properly. Key mistakes are:
- Not applying operations correctly (sign errors).
- Forgetting brackets or order of operations (BODMAS).
- Not substituting the value correctly.
- Comparing expressions without simplifying.
