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Chapter 4: Problem 702

In the following exercises, solve the equation. $$ \frac{m}{-2}=-16 $$

Short Answer

Expert verified
m = 32

Step by step solution

01

Understand the Equation

The given equation is \(\frac{m}{-2} = -16\). The goal is to solve for the variable \(m\).
02

Multiply Both Sides by -2

To isolate \(m\), multiply both sides of the equation by -2. \[ \frac{m}{-2} \times (-2) = -16 \times (-2) \] Simplifying this, we get: \[ m = 32 \]

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Key Concepts

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

Isolating Variables
When solving equations, one of the main goals is to get the unknown variable by itself on one side of the equation. This is known as 'isolating the variable'.
Isolating a variable involves undoing any operations that are currently being applied to it. For example, if a variable is being divided, we use multiplication to undo that division.
In the given equation \(\frac{m}{-2} = -16\), we need to isolate the variable \m\. Here, \m\ is divided by \-2\. To isolate \m\, we must get rid of the \-2\ by performing the opposite operation鈥攎ultiplication.
Multiplication in Equations
Multiplication is a crucial tool for solving equations, especially when a variable is divided by a number. In our example, \(\frac{m}{-2} = -16\), \m\ is divided by \-2\.
To solve, we need to multiply both sides of the equation by \-2\: \[ \frac{m}{-2} \times (-2) = -16 \times (-2) \] This step cancels out the division, leaving the variable isolated. When we multiply the left side, the \-2\ in the denominator and numerator cancel each other out, effectively isolating \m\.
What remains on the left side is just the variable \m\. The right side becomes: \[ -16 \times (-2) = 32 \]
Now, we have \m = 32\, concluding the equation.
Negative Numbers
Working with negative numbers can be confusing, but it becomes easier with practice.
In the equation \(\frac{m}{-2} = -16\), both the divisor and the result are negative.
When multiplying negative numbers, remember:
  • A negative number times a positive number yields a negative result.
  • A negative number times another negative number yields a positive result.
For our equation, multiplying \-16\ by \-2\ gives us a positive result:
\[ -16 \times (-2) = 32 \]
This positive result isolates \m\ successfully. So always pay attention to the signs when performing multiplication or division.

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