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Chapter 5: Problem 290

In the following exercises, solve the equation. $$m+4.6=6.5$$

Short Answer

Expert verified
m = 1.9

Step by step solution

01

- Identify the equation

The given equation is m + 4.6 = 6.5
02

- Isolate the variable

To isolate the variable m, subtract 4.6 from both sides of the equation.
03

- Perform the subtraction

Subtract 4.6 from 6.5: 6.5 - 4.6 = 1.9
04

- Write the solution

After the subtraction, the value of m is: m = 1.9

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Key Concepts

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

Isolating the Variable
In order to solve a linear equation, one of the main tasks is to isolate the variable. This means you need to get the variable you are solving for alone on one side of the equation.

For instance, in the equation:
$$m + 4.6 = 6.5$$
The variable we want to isolate is \(m\).

To do this, we aim to remove any numbers or operations attached to the variable. Once isolated, it becomes much simpler to determine the value of \(m\).

Isolating the variable is a crucial first step in solving any one-variable equation because it simplifies the equation and makes the solution straightforward.
Performing Subtraction
Once you have identified the need to isolate the variable, the next step often involves performing subtraction or addition to either side of the equation.

In our equation: $$m + 4.6 = 6.5$$
We subtract 4.6 from both sides to eliminate the constant term on the left side. This gives us:
$$m + 4.6 - 4.6 = 6.5 - 4.6$$
Performing the subtraction simplifies this to:
$$m = 1.9$$
Subtracting is usually used when you have an addition operation in the equation. It's a fundamental tool for rearranging an equation and isolating the variable.

Remember: Whatever you do to one side of the equation, you should do to the other side to keep it balanced.
One-Variable Equations
The equation we started with is an example of a one-variable equation. This means there is only one unknown, which we call a variable. In our case, we have:
$$m + 4.6 = 6.5$$
One-variable equations are the simplest form of algebraic equations and form the foundation for more complex algebraic operations.

Solving these types of equations involves straightforward steps, mainly:
  • Identifying the variable
  • Isolating the variable by performing arithmetic operations
  • Simplifying the equation to find the value of the variable
By mastering the process of solving one-variable equations, you gain essential problem-solving skills that apply to more advanced areas of algebra. It's all about breaking the problem down into manageable steps and keeping the equation balanced.

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Most popular questions from this chapter

In the following exercises, order each of the following pairs of numbers, using < or >. $$-7.31\underline\quad-7.3$$

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In the following exercises, find the unit rate. Round to two decimal places, if necessary. 8.2 pounds per 3 square inches

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In the following exercises, round each number to the nearest hundredth. $$4.098$$
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