Problem 55 - Prealgebra

Question

Solve each equation. $$3 n-8=-26$$

Step-by-Step Solution

Answer

The solution is \(n = -6\).

Step 1: Add to both sides

To isolate the term with the variable, add 8 to both sides of the equation: \(3n - 8 + 8 = -26 + 8\).This simplifies to \(3n = -18\).

Step 2: Divide both sides

To solve for \(n\), divide both sides of the equation by 3:\(\frac{3n}{3} = \frac{-18}{3}\).This simplifies to \(n = -6\).

Key Concepts

Step-by-Step Solution

When you're faced with solving linear equations, a step-by-step solution is your best friend. It breaks down the problem into manageable parts. This approach helps to tackle each component of the equation separately, ensuring every angle is covered. Let's achieve clarity by looking at the original example, where the equation is: \(3n - 8 = -26\).

• **Step 1:** Add 8 to both sides. This removes the -8 attached to the \(3n\) term, leaving everything nice and simple. When you do the math, it becomes \(3n = -18\).
• **Step 2:** Divide both sides by 3. This separates the \(n\) from the 3, giving us the value of \(n\) directly. This gives us \(n = -6\).

Following these steps carefully ensures accuracy, improving your problem-solving skills and strengthening your math foundation.

Isolating Variables

Isolating variables is a key technique in solving equations. It's all about getting the variable on one side of the equation, by itself. In our example, we need \(n\) to be alone. Why? Because finding the value of \(n\) is our goal! Here's how we did it:
- **Why add 8?** The \(-8\) is subtracted from \(3n\). By adding 8 to both sides, we cancel it out on the left, focusing on \(3n\).- **Next up, division.** With \(3n = -18\), we divide by 3 to isolate \(n\). This action balances our equation and reveals the answer.Keep in mind that isolating the variable not just simplifies your problem, it gives clarity and precision essential for solving equations step by step.

Prealgebra Concepts

Prealgebra concepts are foundational for math learners. They include understanding operations such as addition, subtraction, multiplication, and division applied to find unknown values. In our example, you might recognize some prealgebra basics at work:

• **Handling negatives:** Just like adding and subtracting positives, handle negatives carefully to maintain equation balance.
• **Balancing equations:** Every action applied to one side must be mirrored on the other. This symmetry is crucial for correct solutions.
• **Simplification:** Reduce each step down to a simpler form, making the solution clearer and easier to calculate.

By mastering these prealgebra principles, you build a strong base for more complex math topics in the future. They're simple but essential rules that support your journey through math with confidence and ease.