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LHS and RHS Examples Explained for Maths Success

LHS and RHS Examples Explained for Maths Success

Q: 1. What is rhs and lhs with example?

In mathematics, LHS stands for Left Hand Side and RHS stands for Right Hand Side of an equation. For example, in the equation $2x + 3 = 9$, LHS: $2x + 3$RHS: $9$ Both sides are separated by the equals sign ($=$), which indicates that the value of the LHS is equal to the value of the RHS when $x$ is solved correctly.

Q: 2. What is the difference between lhs and rhs?

The main difference between LHS (Left Hand Side) and RHS (Right Hand Side) lies in their position in an equation. LHS refers to everything on the left side of the equals sign ($=$).RHS refers to everything on the right side of the equals sign. For example, in $y + 5 = 12$, $y + 5$ is the LHS and $12$ is the RHS. This distinction helps students at Vedantu understand and solve equations more efficiently.

Q: 3. How do you verify LHS and RHS?

To verify LHS and RHS in a mathematical equation, substitute the given value(s) of the variable(s) into both sides and simplify: Calculate the value of the LHS using the substituted value.Calculate the value of the RHS.If both results are equal, the equation is verified. For instance, for the equation $2x + 1 = 7$ and $x = 3$, checking: LHS: $2 imes 3 + 1 = 7$RHS: $7$ Since both are equal, the equation holds true. Vedantu students often use this method to check solutions step-by-step.

Q: 4. What is lhs vs rhs?

The LHS (Left Hand Side) and RHS (Right Hand Side) are comparative terms used in equations to describe each part on either side of the equals sign ($=$). LHS: The expression or value before the equals sign.RHS: The expression or value after the equals sign. Understanding this distinction helps Vedantu learners approach algebraic equations with clarity and precision.

Q: 5. What are some examples of equations showing LHS and RHS in algebra?

In algebra, equations consist of a LHS and RHS. Here are common examples: $3x - 4 = 8$: LHS is $3x - 4$, RHS is $8$.$y/2 + 7 = 10$: LHS is $y/2 + 7$, RHS is $10$.$x^2 = 16$: LHS is $x^2$, RHS is $16$. Vedantu provides interactive examples to help students practice identifying LHS and RHS in various algebraic contexts.

Q: 6. How do you solve equations by balancing lhs and rhs?

To solve equations by balancing the LHS and RHS: Perform the same operation on both sides to isolate the variable.Continue simplifying until the variable is alone on one side.The process ensures LHS and RHS remain equal throughout. For example, with $x + 5 = 12$, subtract $5$ from both sides to get $x = 7$. Vedantu tutors guide students step-by-step to develop these essential algebraic skills.

Q: 7. Why is it important to maintain equality between lhs and rhs in mathematical equations?

Maintaining equality between LHS and RHS ensures the integrity of an equation during problem-solving. If any operation is applied to one side, it must also be applied to the other to keep the equation balanced. This concept forms the foundation of algebra, which Vedantu emphasizes to build strong mathematical reasoning in students.

Q: 8. What are common mistakes students make when comparing lhs and rhs?

Common mistakes when comparing LHS and RHS include: Forgetting to apply the same operation to both sides when solving equations.Misplacing terms during transposition.Incorrectly simplifying either the LHS or RHS. Vedantu educators help students avoid these errors through interactive lessons and regular practice.

Q: 9. How are lhs and rhs used in Vedantu's online math classes?

In Vedantu's online math classes, LHS and RHS are introduced early in algebra. Tutors regularly ask students to identify each side, verify solutions, and balance equations in live sessions and assignments. This focus helps students master mathematical concepts and develop confidence for exams.

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Step-by-Step LHS and RHS Example Problems for Easy Practice

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 Examples Explained for Maths Success

1. What is rhs and lhs with example?

In mathematics, LHS stands for Left Hand Side and RHS stands for Right Hand Side of an equation. For example, in the equation $2x + 3 = 9$,

LHS: $2x + 3$
RHS: $9$

Both sides are separated by the equals sign ($=$), which indicates that the value of the LHS is equal to the value of the RHS when $x$ is solved correctly.

2. What is the difference between lhs and rhs?

The main difference between LHS (Left Hand Side) and RHS (Right Hand Side) lies in their position in an equation.

LHS refers to everything on the left side of the equals sign ($=$).
RHS refers to everything on the right side of the equals sign.

For example, in $y + 5 = 12$, $y + 5$ is the LHS and $12$ is the RHS. This distinction helps students at Vedantu understand and solve equations more efficiently.

3. How do you verify LHS and RHS?

To verify LHS and RHS in a mathematical equation, substitute the given value(s) of the variable(s) into both sides and simplify:

Calculate the value of the LHS using the substituted value.
Calculate the value of the RHS.
If both results are equal, the equation is verified.

For instance, for the equation $2x + 1 = 7$ and $x = 3$, checking:

LHS: $2 imes 3 + 1 = 7$
RHS: $7$

Since both are equal, the equation holds true. Vedantu students often use this method to check solutions step-by-step.

4. What is lhs vs rhs?

The LHS (Left Hand Side) and RHS (Right Hand Side) are comparative terms used in equations to describe each part on either side of the equals sign ($=$).

LHS: The expression or value before the equals sign.
RHS: The expression or value after the equals sign.

Understanding this distinction helps Vedantu learners approach algebraic equations with clarity and precision.

5. What are some examples of equations showing LHS and RHS in algebra?

In algebra, equations consist of a LHS and RHS. Here are common examples:

$3x - 4 = 8$: LHS is $3x - 4$, RHS is $8$.
$y/2 + 7 = 10$: LHS is $y/2 + 7$, RHS is $10$.
$x^2 = 16$: LHS is $x^2$, RHS is $16$.

Vedantu provides interactive examples to help students practice identifying LHS and RHS in various algebraic contexts.

6. How do you solve equations by balancing lhs and rhs?

To solve equations by balancing the LHS and RHS:

Perform the same operation on both sides to isolate the variable.
Continue simplifying until the variable is alone on one side.
The process ensures LHS and RHS remain equal throughout.

For example, with $x + 5 = 12$, subtract $5$ from both sides to get $x = 7$. Vedantu tutors guide students step-by-step to develop these essential algebraic skills.

7. Why is it important to maintain equality between lhs and rhs in mathematical equations?

Maintaining equality between LHS and RHS ensures the integrity of an equation during problem-solving. If any operation is applied to one side, it must also be applied to the other to keep the equation balanced. This concept forms the foundation of algebra, which Vedantu emphasizes to build strong mathematical reasoning in students.

8. What are common mistakes students make when comparing lhs and rhs?

Common mistakes when comparing LHS and RHS include:

Forgetting to apply the same operation to both sides when solving equations.
Misplacing terms during transposition.
Incorrectly simplifying either the LHS or RHS.

Vedantu educators help students avoid these errors through interactive lessons and regular practice.

9. How are lhs and rhs used in Vedantu's online math classes?

In Vedantu's online math classes, LHS and RHS are introduced early in algebra. Tutors regularly ask students to identify each side, verify solutions, and balance equations in live sessions and assignments. This focus helps students master mathematical concepts and develop confidence for exams.