Solving a Linear Equation | Steps to Isolate and Find the Value of x

5x + 4 = 31 + 2x

To solve the equation 5x + 4 = 31 + 2x, we need to isolate the variable x on one side of the equation

To solve the equation 5x + 4 = 31 + 2x, we need to isolate the variable x on one side of the equation.
First, we can simplify the equation by combining like terms. We do this by subtracting 2x from both sides of the equation:
5x + 4 – 2x = 31 + 2x – 2x
This simplifies to:
3x + 4 = 31

Next, we want to isolate the term with x by moving the constant term to the other side of the equation. We do this by subtracting 4 from both sides:
3x + 4 – 4 = 31 – 4
This simplifies to:
3x = 27

Finally, we need to solve for x by dividing both sides of the equation by the coefficient of x, which is 3:
3x/3 = 27/3
This simplifies to:
x = 9

Therefore, the solution to the equation 5x + 4 = 31 + 2x is x = 9.

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Definitions:

1. Variable: In mathematics, a variable is a symbol that represents an unknown quantity or a value that can change. It is commonly denoted by letters such as x, y, or z.

2. Equation: An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), which are connected by an equal sign (=).

3. Coefficient: In an algebraic expression or equation, the coefficient is the numerical factor of a variable. It is the number that multiplies the variable. For example, in the equation 2x + 3 = 7, the coefficient of x is 2.

4. Simplify: Simplifying an expression or equation involves reducing it to its simplest or most compact form by combining like terms or performing arithmetic operations.

5. Isolate: In mathematics, isolating a variable means to manipulate an equation or expression in order to have the variable appear on one side of the equation or expression by itself.

I hope this explanation and definitions clarifies things for you. Let me know if you have any further questions!

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