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Chapter 5: Problem 613

In the following exercises, solve. $$ -8.6 x=34.4 $$

Short Answer

Expert verified
x = -4

Step by step solution

01

Understand the Equation

The given equation is \( -8.6x = 34.4 \). This is a basic linear equation where the goal is to find the value of \( x \).
02

Isolate the Variable

To isolate \( x \), divide both sides of the equation by \(-8.6\). This will give: \[\frac{-8.6x}{-8.6} = \frac{34.4}{-8.6}\]
03

Simplify Both Sides

Simplify the equation from Step 2. The left side simplifies to \( x \) since \( -8.6 / -8.6 = 1 \). The right side simplifies to \[ x = \frac{34.4}{-8.6} = -4 \].

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Key Concepts

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

Isolate the Variable
In a linear equation, our goal is to find the value of the unknown variable. To do this, we need to isolate the variable on one side of the equation.

For example, consider the equation \( -8.6x = 34.4 \).

To isolate \( x \, \) we need to perform operations to move everything else to the other side of the equation.
Divide Both Sides
In many linear equations, you need to use division to isolate the variable. To cancel out the coefficient of the variable, we divide both sides of the equation by that coefficient.

Let's go through it step by step:
  • Given equation: \(-8.6x = 34.4\)
  • To get \(x\) alone, divide both sides by \(-8.6\): \[ \frac{-8.6x}{-8.6} = \frac{34.4}{-8.6} \]

This process ensures that the equation remains balanced, meaning both sides of the equation are equal. Now, the left side simplifies to \(x\).

Simplify
After isolating the variable and dividing both sides, the next step is to simplify the equation to find the value of \(x\).

Using the example again:
  • \(\frac{-8.6x}{-8.6} = \frac{34.4}{-8.6} \)
  • The left side simplifies to \(x\), because \( \frac{-8.6x}{-8.6} = 1x = x\).

Now, simplify the right side:
  • Calculate \( \frac{34.4}{-8.6} = -4 \).

Therefore, the solution is \( x = -4 \).

We can see that simplifying both sides correctly yields the final value of the variable, solving the equation.

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