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Chapter 8: Problem 23

In the following exercises, solve each equation. $$ m+6-8=15 $$

Short Answer

Expert verified
m = 17

Step by step solution

01

Simplify the Equation

First, simplify the equation by combining like terms. Given the equation: t. Calculate 6-8 to get -2. The equation becomes: \[ m - 2 = 15 \].
02

Isolate the Variable

Add 2 to both sides of the equation to isolate the variable m. The equation now is: \[ m - 2 + 2 = 15 + 2 \]which simplifies to: \[ m = 17 \].

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Key Concepts

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

Combining Like Terms
Combining like terms is an important skill when solving linear equations.
This involves adding or subtracting terms that have the same variable or are constants (numbers without variables).
In the given equation, the terms 6 and 8 are like terms because they are both constants.
To simplify, subtract 8 from 6 to get -2.
This reduces the original equation from \( m+6-8=15 \) to \( m-2=15 \).

When you combine like terms, you are simplifying the equation, making it easier to solve.
Isolating the Variable
Now that you have simplified the equation to \( m-2=15 \), the next step is to isolate the variable.
Isolating the variable means getting the variable (here, m) by itself on one side of the equation.
To do this, perform the opposite operation of what is being done to the variable.
In this case, m has -2 subtracted from it.
To isolate m, add 2 to both sides of the equation.
This results in \( m-2+2=15+2 \), and simplifies to: \( m=17 \).
Now the variable m stands alone, meaning we have successfully isolated it.
Equation Simplification
Equation simplification is the process of making an equation easier to solve by performing basic arithmetic operations.
This could involve combining like terms, as we saw earlier, and performing other operations like addition or subtraction.
The goal of simplification is to make the equation as straightforward as possible, so you can quickly find the solution.
In our example, we started with \( m+6-8=15 \).
After combining like terms and isolating the variable, we simplified the equation to \( m=17 \).
When you simplify an equation correctly, solving it becomes much easier and less error-prone.

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