What is the first step in solving an equation using logical sequencing?

The first step in solving an equation using logical sequencing is to simplify both sides of the equation.

Understanding the First Step: Simplifying the Equation

Before you can effectively isolate a variable or combine like terms, you need to ensure both sides of the equation are in their simplest form. This often involves:

• Combining like terms: On each side of the equation, group and combine terms that share the same variable and exponent, or are simply constant values.
• Distributing: If there are parentheses, use the distributive property to multiply the term outside the parentheses by each term inside.

This initial simplification makes the equation easier to manipulate and reduces the chances of making errors later in the solving process.

Detailed Breakdown of Simplifying

Combining Like Terms:

This involves adding or subtracting terms that have the same variable raised to the same power (e.g., 3x and 5x) or constant terms (e.g., 7 and -2).

• Example: If you have the expression 2x + 3 + 4x - 1, you would combine 2x and 4x to get 6x and combine 3 and -1 to get 2. The simplified expression becomes 6x + 2.

Distribution:

The distributive property states that a(b + c) = ab + ac. Applying this property removes parentheses, allowing you to combine like terms afterward.

• Example: If you have the expression 3(x + 2), you would distribute the 3 to both x and 2, resulting in 3x + 6.

Why Simplifying is Crucial

Simplifying first makes the subsequent steps, like moving and combining terms, much easier. A complex, unsimplified equation is more prone to errors. By tidying up each side initially, you reduce the cognitive load and increase accuracy.

According to reference material, the steps in solving an equation involve:

1. Simplify both sides of the equation.
2. Move and combine like terms to one side.

This emphasizes the importance of simplification as the foundational step.