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Chapter 2: Problem 15

Solve each equation using the Subtraction and Addition Properties of Equality. $$m-18=-200$$

Short Answer

Expert verified
m = -182

Step by step solution

01

Understand the Equation

The equation given is: \[m - 18 = -200\] The goal is to solve for the variable \(m\).
02

Apply the Addition Property of Equality

To isolate \(m\), add 18 to both sides of the equation. \[m - 18 + 18 = -200 + 18\]
03

Simplify the Equation

Simplify both sides to find the value of \(m\): \[m = -200 + 18\] \[m = -182\]

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Key Concepts

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

Addition Property of Equality
When solving equations, the Addition Property of Equality is very useful. This property states that if you add the same amount to both sides of an equation, the equation remains balanced.
For example, if you have an equation like \(m - 18 = -200\), you need to get rid of the \(-18\) on the left side to isolate the variable \(m\).
To do this, you add \(+18\) to both sides of the equation:

- First side: \(m - 18 + 18\)
- Second side: \(-200 + 18\)

By adding these numbers, you simplify the left side to just \(m\) and change the right side accordingly.
This process ensures that both sides of the equation remain equal, leading us closer to the solution.
Subtraction Property of Equality
The Subtraction Property of Equality is similar to the Addition Property but involves subtraction. It says that subtracting the same amount from both sides of an equation keeps it balanced.
In the given problem, the first step is already set up for addition because the initial equation \(m - 18 = -200\)
However, if you need to use subtraction to isolate the variable in other problems, the principle is just as straightforward:

- Suppose you have \(+18\) instead of \(-18\)
- You would subtract \(+18\) from both sides to cancel it out:


This principle keeps equations valid while simplifying the process to find the variable's value.
Isolate Variable
Isolating the variable is the main goal when solving an equation. It means getting the variable by itself on one side of the equation.
In our example \(m - 18 = -200\), you need to get \(m\) alone to find its value.

Steps:

  • Add 18 to both sides: \(m - 18 + 18 = -200 + 18\)
  • Simplify both sides to isolate \(m\):
    \(m = -200 + 18\)
    \(m = -182\)

Now you have isolated \(m\), and the equation is solved. The value of \(m\) is \(-182\). This approach can be applied to more complex equations, but the core principle remains the same: simplify and isolate the variable to find its value.

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