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Chapter 5: Problem 606

In the following exercises, solve. $$ m+3.8=7.5 $$

Short Answer

Expert verified
m = 3.7

Step by step solution

01

Identify the Equation

The given equation is: \[ m + 3.8 = 7.5 \]
02

Isolate the Variable

To solve for \( m \), isolate \( m \) on one side of the equation. Subtract 3.8 from both sides: \[ m + 3.8 - 3.8 = 7.5 - 3.8 \]
03

Simplify Both Sides

Simplify the equation after performing the subtraction: \[ m = 3.7 \]

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Key Concepts

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

Isolating Variables
In the equation \( m + 3.8 = 7.5 \), our main goal is to solve for the variable \( m \). This means we need to get \( m \) by itself on one side of the equation. To do this, we use a process called isolating the variable.
Here are the steps to isolate the variable:
  • Look at the equation and see what operations are being performed on the variable you want to isolate. In our case, adding 3.8 to \( m \).
  • Perform the opposite, or inverse, operation to both sides of the equation. Since the variable \( m \) is being added to 3.8, we need to subtract 3.8 from both sides to cancel it out.
This will give us:
\( m + 3.8 - 3.8 = 7.5 - 3.8 \)
which simplifies to \( m = 3.7 \). This is how isolating the variable works in basic linear equations.
Basic Arithmetic
Basic arithmetic involves simple operations like addition, subtraction, multiplication, and division. When solving linear equations, these operations help us to simplify and find the value of the variable.
Let's review some key points:
  • Addition: Combining numbers to get a sum. For example, \( 3 + 4 = 7 \).
  • Subtraction: Taking one number away from another. For example, \( 7 - 2 = 5 \).
  • In our equation, the basic arithmetic step involves subtraction: \( 7.5 - 3.8 = 3.7 \).
  • It's crucial to perform the same operation on both sides of the equation to keep it balanced.
By understanding these basic arithmetic steps, we ensure that we manipulate the equation correctly to solve for the variable.
Simplifying Equations
Simplifying an equation means making it as straightforward as possible. After we've isolated the variable and performed basic arithmetic, we need to simplify.
In our example, after subtracting 3.8 from both sides, the equation becomes:
\( m + 3.8 - 3.8 = 7.5 - 3.8 \)
This simplifies further to:
\( m = 3.7 \)
Simplification steps often include:
  • Combining like terms, if any.
  • Reducing fractions or performing operations to get the simplest form.
  • Ensuring the variable is isolated and all other terms are moved to the opposite side.
By simplifying equations, we make it easier to see the solution clearly. In our exercise, \(m = 3.7\) is the simplified and final form.

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