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# RHS|Definition & Meaning

## Definition

RHS is an **acronym** for Right **Hand** Side. In math, this refers to **everything** on the right side of the equal **sign** (=) in an equation. When **solving** equations, we perform a series of **mathematical manipulations** and **operations** between the left and right-hand sides to get the **result.** While it is not a rule, we usually write the final result on the **RHS** as the **last** step of the solution.

**Right-hand Side**

When we have an **equation,** we are **able** to split it into two **components,** which are **referred** to as the **left-hand** side and the **right-hand** side. The left and right-hand sides of an equation are often **abbreviated** as LHS and **RHS.**

The **term** can refer to either an **equation** or an inequality; the right-hand side of an **expression** is **anything** that is located on the **right** side of a **test** operator, and the **left-hand** side (LHS) is **defined** in the same **manner.** Note that in **mathematics,** it is **customary** to refer to the sides of an **equation** as “the left-hand side” and “the **right-hand** side.”

For **example,** when talking about:

**𝑐 _{2}=𝑎_{2}+𝑏_{2}**

It is **more** likely that **someone** will tell you that “the right-hand side is a_{2}+b_{2}” rather than just saying that “the right side is a_{2}+b_{2}.” In **mathematical** writing, the **expressions** “right-hand side” and **“left-hand** side” are frequently abbreviated to “RHS” and “LHS”, **respectively.**

In a **chemical equation,** the term “reactant” **refers** to the material or substances that are located to the left of the arrow. The **component** that is present at the **beginning** of a chemical reaction is referred to as a reactant. Products are whichever material or **substances** may be found to the right of the arrow.

**Equations and Sides of Equations**

**Equations** are a type of **mathematical statement** that contain two **algebraic expressions** on each side of an “equal to” sign (=) in the middle of the **statement.** It **illustrates** the **relationship** of equality that exists between the expressions written on the left side and the **expression** written on the right side by **placing** them side by side.

The **left-hand** side equals the right-hand side is a **condition** that must be **satisfied** in every mathematical equation. **Equations** can be solved so that the **value** of a missing variable, which **stands** for a **missing** quantity, can be determined.

In a statement, the absence of the symbol for “equal to” indicates that the **statement** is not an equation. It will be **understood** that you are making an **expression.**

If we **obtain** both the **left-hand** side (LHS) and the right-hand side **(RHS)** to have the same value, we may declare that the equation is true; otherwise, we cannot say that the equation is true for at least **some** values of real **numbers.**

**Example 1: (x + y) ^{2 }= x^{2 }+ 2xy + y^{2}**

Where **LHS** = (x + y)^{2} and **RHS** = x^{2 }+ 2xy + y^{2}

**Example 2: (x + y)(x − y) = x ^{2 }− y^{2}**

**Where LHS** = (x + y)(x − y) and **RHS = x ^{2 }− y^{2}**

A **mathematical** equation is a **compound expression** that **consists** of two expressions connected by an **equals** sign, **indicating** that **whatever** is written on the left side of the sign is equivalent to whatever is put on the **right** side of the equals sign. An **equation** is a **mathematical** term.

** Left-Hand** Side (LHS) **expression** = **Right-Hand** Side (RHS) **expression**

This **expression** can be **anything** from a single **variable** to a constant to a **polynomial** to a logarithmic **amount** or **anything** else you can **think** of.

We **have** two **options** at our disposal **whenever** we need to **demonstrate** that a given **equation** or identity is **correct:** Find the value on one side of the equal sign on one side of the **equation** using the **information** from the other side, and if they are equal, the **equation** is **correct.**

**Simplify** both **Left Hand Side(LHS)** and the **Right-Hand side(RHS)** until **both** of them become the same. Then LHS will be equal to RHS, which is **written** as LHS= RHS, i.e., **identity** or **mathematical** approved fact is true.

**Simplify** the **Left** Hand Side (LHS) as well as the Right Hand **Side** (RHS) until they are **identical** in **appearance.** Then the LHS will be the same as the **RHS,** which may be **represented** as LHS= RHS, which indicates that the **identity** or **mathematically** proven fact is correct.

**Because** one side **may** be derived from the other using appropriate **mathematical** processes, the **equality sign** on the left-hand side of the **equation** indicates that both sides are **equivalent** to one **another.**

## Homogeneity of Equations

In the process of **solving mathematical equations,** in **particular** linear simultaneous equations, differential equations, and **integral** equations, the term **“homogeneous”** is frequently used for **equations** that have some linear operator L on the left-hand side (LHS) and 0 on the **right-hand** side (RHS).

In contrast, an equation is said to be inhomogeneous or non-homogeneous if its right-hand side **(RHS)** does not equal zero, as **shown** by the **following:**

**Lf = g,**

This **equation** has to be **solved** in order to find f, given that g is a fixed function. **Therefore,** a solution to an inhomogeneous equation can have a **solution** to a homogeneous equation added to it and **still** be considered a **solution** to the **inhomogeneous** problem.

The **inhomogeneous** equation **requires** more **realistic solutions** with **some** matter or charged particles, whereas the **homogeneous** equation may **correspond** to a physical theory that was **stated** in empty space.

## Solving an Equation

An **equation** can be **thought** of as a weighing scale in which both sides have the same amount of weight. It does not **matter whether** we add or **remove** the same number from both sides of an **equation;** the **result** will always be the same.

In a **similar** vein, **even** if we multiply or **divide** the same number into both **sides** of an equation, the equation will still be correct. Take into **consideration** the equation of a line, which is 3x **minus** 2 **equals** 4.

To **maintain** the integrity of the **equilibrium,** we shall conduct **mathematical** operations on **both** the left and right-hand sides. Let’s **reduce** the left-hand side to 3x by adding 2 to both sides. This **won’t** throw off the **equilibrium** at all. The new **lower horizontal** scale is 3x 2 + 2 = 3x, and the new upper horizontal scale is 4 + 2 = 6.

Therefore, the **equation** may be **rewritten** as 3x = 6 First, let’s **divide** both sides by 3, which will bring the left-hand side down to x. Therefore, the answer to the **equation** that describes a line is x equal to 2.

The following are the **actions** that **need** to be taken to solve a fundamental equation with one variable (linear):

The first step is to apply **arithmetic operations** to both sides of the **equation, which** will move all of the terms that contain **variables** to one side of the **equation** and all of the **constants** to the other side.

The second step is to **combine** all like words by adding or removing them. Terms are terms that contain the same variable with the same **exponent.**

**Break** it down into its **simplest** form and get the **answer.**

## An Example of RHS

**How** many **eggs** do we have in the given **illustration** for the **RHS? **Is the equation correct? If it is incorrect, how would you fix it?

### Solution

In the **given** illustration, we have **6** **eggs** in the RHS. Since 2 eggs on the LHS are not equal to 6 eggs on the RHS, this equation is also incorrect. To fix it, we’d need to add 4 eggs or multiply by 3 on the LHS to balance both the sides.

*All mathematical drawings and images were created with GeoGebra.*