91Ó°ÊÓ

Solving an equation usually means finding the value of the variable that makes the equation true. In the context of our example, we need to solve for \( x \) in the equation \( 74x - 6 = 91 \). To tackle this, we'll use a systematic approach which often involves simplifying and rearranging terms to isolate the variable on one side of the equation.

Equations are all about balance. Think of the equal sign as a delicate scale. Whatever you do to one side of the equation, you must do the same to the other to keep it balanced. Here's a simple checklist for solving equations:

• Look at the equation and identify operations affecting the variable.
• Use inverse operations to simplify terms and isolate the variable.
• Check your solution by substituting the variable's value back into the original equation.

This will enhance your confidence in solving equations, ensuring accurate results by verifying your solution is correct.

When solving equations, isolating the variable means getting the variable alone on one side of the equation. This is an essential step to solve for the unknown. Let's take our example: \( 74x - 6 = 91 \). Here, \( x \) is the variable we need to isolate.

The first step is to remove any constants from the side of the equation with \( x \). In our exercise, the constant is \(-6\). To cancel it out, we use the opposite operation, which is addition:

• Add 6 to both sides: \( 74x - 6 + 6 = 91 + 6 \).
• After simplifying, the equation becomes \( 74x = 97 \).

Now, the term with \( x \) is isolated, which makes our equation simpler and prepares it for the next step.

Once the variable term is isolated, often the last step in solving equations involves division, especially if the term is multiplied by a coefficient. In our example, we're left with \( 74x = 97 \) after isolating \( x \).

To find the value of \( x \), we need to get rid of the coefficient \( 74 \). This is done by performing division:

• Divide both sides by 74: \( x = \frac{97}{74} \).

This division step allows you to solve for \( x \).

Ensuring each step involves performing the same operations on both sides of the equation keeps it balanced, preserving its integrity. This method confirms that the value of \( x \) satisfies the original equation.