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Chapter 2: Problem 43

Solve. $$ 7 x+3=0 $$

Short Answer

Expert verified
\( x = -\frac{3}{7} \)

Step by step solution

01

Isolate the variable term

To solve for \( x \), we need to isolate the term that contains the variable. Start by subtracting \( 3 \) from both sides of the equation:\[ 7x + 3 - 3 = 0 - 3 \]Simplifies to:\[ 7x = -3 \]
02

Solve for the variable

Now, divide both sides by \( 7 \) to solve for \( x \):\[ \frac{7x}{7} = \frac{-3}{7} \]Therefore, \( x = -\frac{3}{7} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Variable
The goal of isolating a variable in an equation is to get the variable by itself on one side. Think of it as clearing away anything that's keeping the variable from standing alone. In the equation given, \(7x + 3 = 0\), we want \(x\) by itself.

**How to Isolate the Variable:**
  • Identify the term that contains the variable. Here it is \(7x\).
  • Move other numbers away from the variable. In this case, we subtract \(3\) from both sides to remove the \(+3\) next to the \(x\).
  • Ensure you perform the same operation on both sides to maintain balance in the equation.
After subtracting \(3\), we reach \(7x = -3\). Now, \(x\) is closer to being isolated. Next, we'll make \(x\) completely by itself in the next step.
Solving Equations
With the variable almost isolated, our next task is to get \(x\) completely by itself. To do this, divide by the number that鈥檚 multiplying the variable.

**Final Steps for Solving:**
  • Divide both sides of the equation by \(7\), as it's the number in front of \(x\).
  • This leaves \(x\) isolated: \[ \frac{7x}{7} = \frac{-3}{7} \]
  • The result is \(x = -\frac{3}{7}\).
This process of dividing ensures that you accurately solve for \(x\). It鈥檚 important to remember to perform the same operation on both sides of the equation, ensuring everything stays balanced.
Step by Step Solution
Understanding how to solve equations step by step allows you to tackle a wide array of problems with confidence. Following a set path leads to finding solutions efficiently.

**Why a Step by Step Approach Works:**
  • Each step simplifies the problem and reduces errors.
  • You ensure each equation remains balanced, crucial for arriving at the correct answer.
  • Breaking the problem into smaller parts makes complex equations manageable.
By separating the problem into steps鈥攆irst isolating the variable and then solving鈥攚e make the solution process clear and logical. Practice this method, and solving linear equations will become second nature!

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