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Chapter 5: Problem 294

In the following exercises, solve the equation. $$ b+5.8=-2.3 $$

Short Answer

Expert verified
b = -8.1

Step by step solution

01

Subtract 5.8 from Both Sides

To isolate the variable, start by subtracting 5.8 from both sides of the equation: \[ b + 5.8 - 5.8 = -2.3 - 5.8 \]
02

Simplify Both Sides

Solving the above, we get: \[ b = -2.3 - 5.8 \]
03

Calculate the Right Side

Compute the value on the right side of the equation: \[ b = -8.1 \]

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Key Concepts

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

Isolating the variable
When solving linear equations, one of the first steps is to isolate the variable. In our exercise, the variable is \ b \.
This means we want to get \ b \ by itself on one side of the equation.
Starting with the equation \ b + 5.8 = -2.3 \, our goal is to eliminate the constant term added to \ b \.

To do this, we use the opposite operation: subtraction. By subtracting 5.8 from both sides of the equation, we keep the equation balanced.
The updated equation will be:

\[ b + 5.8 - 5.8 = -2.3 - 5.8 \]

This step is crucial because it helps in reducing the equation to a simpler form, ensuring that the variable \ b \ stands alone.
Arithmetical operations
Arithmetical operations are essential when manipulating equations. These include addition, subtraction, multiplication, and division.
To solve the equation \ b + 5.8 = -2.3 \, we used subtraction as the main operation.

Let's break it down:
  • We subtracted the same value, 5.8, from both sides of the equation to maintain balance.
  • This operation doesn't change the equation's equality; it only simplifies it.

Now, both sides of the equation are:
\[ b = -2.3 - 5.8 \]

Here, subtraction on the right side combines the terms, which leads us to our next step鈥攕implification.
Simplification in equations
Simplification in equations means reducing them to their simplest form. For our exercise, we need to simplify \ -2.3 - 5.8 \.
We perform this subtraction step-by-step:

1. Recognize both numbers are negative.
2. Combine their absolute values: \ 2.3 + 5.8 = 8.1 \.
3. Since both numbers were negative, the combined result is also negative.
So we have:
\[ b = -8.1 \]
By simplifying, we find the value of the variable \ b \. Finally, the equation is solved with \ b = -8.1 \.

This simplified result tells us the precise value that satisfies the original equation.

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