How to Solve the Equation 2(3x + 1) = 7x – 5 Step by Step | Math Tutorial

2 (3x + 1) = 7x – 5

To solve the equation 2(3x + 1) = 7x – 5, we will use the distributive property and simplify both sides of the equation

To solve the equation 2(3x + 1) = 7x – 5, we will use the distributive property and simplify both sides of the equation.

First, distribute the 2 to each term inside the parentheses:
6x + 2 = 7x – 5

Now, let’s gather all the x terms on one side of the equation by subtracting 6x from both sides:
2 = 7x – 6x – 5

Simplifying further gives:
2 = x – 5

Next, let’s isolate the x variable by adding 5 to both sides of the equation:
2 + 5 = x – 5 + 5

Simplifying gives:
7 = x

Therefore, the solution to the equation 2(3x + 1) = 7x – 5 is x = 7.

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Definitions:

1. Equation: An equation is a mathematical statement that shows the equality of two expressions. It consists of an equal sign (=) between two expressions, called the left-hand side (LHS) and the right-hand side (RHS). The goal is to find the value(s) of the variables that satisfy the equation.

2. Distributive Property: The distributive property is a mathematical property that allows us to multiply a value by a group of terms inside parentheses. It states that for any real numbers a, b, and c, a(b + c) = ab + ac. This property is commonly used to simplify expressions or solve equations by distributing a value to each term inside parentheses.

3. Simplifying: Simplifying refers to the process of reducing or transforming an expression, equation, or any mathematical object into its simplest or most concise form. This is often done by combining like terms, applying mathematical properties, or performing operations such as addition, subtraction, multiplication, or division. The goal is to express the given expression or equation in a more manageable or understandable way.

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