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Literal Equation Calculator + Online Solver With Free Steps

The online Literal Equation Calculator is a calculator that solves a literal equation in terms of a specific variable.

The Literal Equation Calculator is an easy-to-use calculator that helps scientists and mathematicians quickly derive formulas from an equation.

What Is a Literal Equation Calculator?

A Literal Equation Calculator is an online calculator that allows you to solve literal equations by isolating a single variable.

The Literal Equation Calculator requires three input values: the left side of the equation, the right side of the formula, and the variable we need to isolate.

After inputting the results, the Literal Equation Calculator can solve the equation using the isolated variable.

How To Use a Literal Equation Calculator?

To use the Literal Equation Calculator, enter the inputs into the calculator and click the “Submit” button.

The detailed instructions on how to use the Literal Equation Calculator are given below:

Step 1

First, enter the equation’s left side into the Literal Equation Calculator.

Step 2

After entering the equation’s left side, you enter the right side of the equation into the Literal Equation Calculator.

Step 3

After entering both sides of the equation, enter the variable we want to isolate from the equation. We enter this variable into the Literal Equation Calculator.

Step 4

Once we are done inputting all the required information into our Literal Equation Calculator, click the “Submit” button. The calculator will instantly solve the literal equation according to the isolated variable selected and display the results in a new window.

How Does a Literal Equation Calculator Work?

A Literal Equation Calculator works by taking in both the left and right parts of the equation and shifting them onto one side of the equation. The isolated variable is moved to the other side of the equation. 

The following equation is an example:

\[ A = \pi r^{2} \]

Where: 

A = Area of the circle 

pi = Constant 

r = Radius of the circle 

What Is an Equation?

Equations are mathematical statements that contain two algebraic equations on each side of an equal sign (=). It depicts the equal link between the expression written on the left side and the expression written on the right side.

L.H.S = R.H.S (left hand side = right hand side) appears in every mathematical equation. Equations can calculate the value of an unknown variable representing an unknown quantity. It is not an equation if the statement contains no ‘equal to’ symbol. It shall be taken into account as an expression.

Coefficients, variables, operators, constants, terms, expressions, and an equal to sign are all components of an equation. When we compose an equation, we must include a $= $ symbol and terms on both sides. Both sides should be treated equally. 

An algebraic equation contains variables in it. The following equation is an example of an algebraic equation:

2x + 9 = 24 

What Is a Literal Equation?

Literal equations are equations that use letters and alphabets. Literal equations consist of variables where each variable represents a quantity or meaning.

The area of a square is given by the formula $A = s^{2}$, where s signifies the length of a side of the square and A denotes its area. This is an example of a literal equation.

For instance, the perimeter of a square is given by the equation P = 4s, where P is the square’s perimeter, and s is its side length. Sometimes, equations are presented to us as formulas for geometric shapes. P and s are variables that allow for the expression of P in terms of s. A literal equation looks like this. We cannot determine a variable’s precise numerical value in literal equations.

Literal equations have two or more variables (such as letters or alphabets), each of which can be represented in terms of one or more additional variables.

One variable must be isolated to solve literal equations, and the solution must be expressed clearly in terms of the other variables. In a literal equation, each variable denotes a certain amount.

Formula For Literal Equations

The formula for literal equations is not fixed. If an equation contains multiple unique variables, we can recognize it as a literal equation. Linear, quadratic, cubic, etc., can all be literal equations. 

Literal equations can be solved by clearly expressing each variable in the equation in terms of the other variables. 

An equation might not be a literal equation if the same variable appears in the equation in multiple ways. The equation $x^{3}+2x^{2}-x+3=0$ is not a literal equation because it only has one variable, x, but it does so in various ways. This equation contains x as the sole variable.

Usage

Literal Equations are frequently used in mathematical and scientific formulations. Examples of literal equations include:

  • A circle’s surface area equals $\pi r^{2}$. This literal equation has two variables, A and r, where A is the area and r is the radius.
  • $E = mc^{2}$ is the mass-energy equation. This literal equation has three variables: E, m, and c, and each variable represents a physical quantity.
  • $V = (\frac{4}{3})\pi r^{3}$ is the volume of a sphere. This literal equation has two variables, A and r, where V is the volume and r is the radius.
  • x + y = 1 is an algebraic equation. This literal equation contains two variables, x, and y.

Solved Examples

The Literal Equation Calculator instantly solved your literal equation by isolating a single variable. 

The following examples are solved using the Literal Equation Calculator:

Example 1

While working on an assignment, a college student comes across the following equation:

T = 2 $\pi$ R(R+h) 

To solve his assignment, the student must solve this literal equation by isolating h. Using the Literal Equation Calculator solve this equation for h.

Solution

We can use the Literal Equation Calculator to quickly solve this literal equation for h. First, we enter the left side of the equation into the Literal Equation Calculator; the left side of the equation is T. After entering the equation’s left side, we enter the equation’s right side into the Literal Equation Calculator; the right side of the equation is 2 $\pi$ R(R+h). Once we enter the equations, we type in the variable we need to isolate in the Literal Equation Calculator; the variable we need to separate is h.

Finally, once all the inputs are entered into the Literal Equation Calculator, we click the “Submit” button. The calculator immediately provides you with the results in a separate window.

The following results are taken from the Literal Equation Calculator:

Input Interpretation:

Solve:

T = 2 $\pi$ R(R+h) for h 

Result:

\[ h = \frac{T}{2 \pi R}-R \ and \ R \neq 0 \]

Example 2

While conducting his research, a mathematician comes across the following equation:

\[ A = \frac{\pi r^{2} S}{360} \]

To complete his research, the mathematician has to isolate the variable S in the given literal equation. With the help of the Literal Equation Calculator, solve the literal equation for the variable S.

Solution

We can simply answer this literal equation for S using the Literal Equation Calculator. First, we enter the equation’s left side, A, into the Literal Equation Calculator. After inputting the left half of the equation, we enter the right side of the equation into the Literal Equation Calculator; the right side of the equation is $\frac{\pi r^{2} S}{360}$. After entering the equations, we use the Literal Equation Calculator to isolate the variable; the variable we need to isolate is S.

Finally, after entering all inputs into the Literal Equation Calculator, we click the “Submit” button. The calculator displays the findings in a different window right away.

The following results are generated using the Literal Equation Calculator:

Input Interpretation:

Solve:

\[ A = \pi r^{2} \times \frac{S}{360} \ for \ S \]

Results:

\[ S = \frac{360A}{\pi r^{2}} \ and \ r \neq 0 \]

Example 3

A scientist comes across the following equation:

Q = 3a + 5ac 

The scientist needs to solve this equation by isolating the variable a. Using the Literal Equation Calculator, solve the literal equation by isolating the variable a.

Solution

We may quickly answer this literal equation for the variable a using the Literal Equation Calculator. First, we enter the left side of the equation into the Literal Equation Calculator; the left side of the equation is Q. After inputting the equation’s left side, we enter the equation’s right side into the Literal Equation Calculator; the right side of the equation is Q = 3a + 5ac. After entering the equations, we enter the variable we need to isolate into the Literal Equation Calculator; the variable to be separated is a.

We press the “Submit” button after entering all the data into the Literal Equation Calculator. You get the results from the calculator right away in a separate window.

The following results are extracted from the Literal Equation Calculator:

Input Interpretation:

Solve:

Q = 3a + 5ac for a 

Results:

\[ a = \frac{Q}{5c + 3} \ and \ 5c + 3 \neq 0 \]

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