Solving the Equation 3(5x – 2) + 2 = 26 Using Order of Operations

3 (5x – 2) + 2 = 26

To solve the equation 3(5x – 2) + 2 = 26, we will follow a step-by-step process known as order of operations

To solve the equation 3(5x – 2) + 2 = 26, we will follow a step-by-step process known as order of operations.

Step 1: Distribute
In this step, we are going to distribute the 3 to both terms inside the parentheses.
3 * 5x = 15x
3 * (-2) = -6

After distributing, the equation becomes:
15x – 6 + 2 = 26

Step 2: Combine like terms
In this step, we combine the constant terms (-6 and 2) on the left side of the equation.
15x – 4 = 26

Step 3: Get the variable term alone
In this step, our goal is to isolate the variable term (15x) on one side of the equation. To do this, we will manipulate the equation by using inverse operations.

First, we add 4 to both sides of the equation to isolate the variable term.
15x – 4 + 4 = 26 + 4
15x = 30

Step 4: Solve for x
Now, to find the value of x, we divide both sides of the equation by 15.
(15x)/15 = 30/15
x = 2

Solution:
The value of x that satisfies the equation 3(5x – 2) + 2 = 26 is x = 2.

Definitions:

1. Equation: An equation is a mathematical statement with an equal sign (=) that indicates two expressions are equal. Equations are used to find the value of unknown variables.

2. Distributive Property: The distributive property is a fundamental property of mathematics that allows you to multiply a number by a group of terms contained within parentheses. It states that when you multiply a number by a sum or difference within parentheses, you can distribute the number to each term inside the parentheses.

3. Order of Operations: The order of operations is a set of rules used to clarify the sequence in which mathematical operations should be performed in an expression or equation. The order is as follows: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

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