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Chapter 2: Problem 16

Solve each equation using the Subtraction and Addition Properties of Equality. $$m-12=-12$$

Short Answer

Expert verified
The solution is \( m = 0 \).

Step by step solution

01

Identify the Equation

The given equation is: \[ m - 12 = -12 \]
02

Use the Addition Property of Equality

To isolate the variable \( m \), add 12 to both sides of the equation:\[ (m - 12) + 12 = -12 + 12 \]
03

Simplify Both Sides

Simplify the equation by performing the addition:\[ m = 0 \]
04

Verify the Solution

To verify, substitute \( m = 0 \) back into the original equation and check if both sides are equal:\[ 0 - 12 = -12 \]Both sides are equal, so \( m = 0 \) is the correct solution.

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Key Concepts

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

Addition Property of Equality
One important concept when solving linear equations is the Addition Property of Equality. This property states that if you add the same number to both sides of an equation, the equality of the equation is maintained. This is extremely helpful when you need to isolate a variable. For example, in the equation \(m - 12 = -12\), to isolate the variable \(m\), we add 12 to both sides of the equation:

\ (m - 12) + 12 = -12 +12 \
This way, the equation simplifies to \ m = 0 \: the variable is isolated, and we have our solution.

Remember, when using the Addition Property of Equality:
  • Make sure what you add to one side, you also add to the other side.
  • This helps keep the equation balanced.
Subtraction Property of Equality
Another key concept in solving linear equations is the Subtraction Property of Equality. This property is like the addition property but involves subtraction. It states that if you subtract the same number from both sides of an equation, the equality remains unchanged. For instance, if our equation was \(m + 12 = 0\), to isolate \(m\), we would subtract 12 from both sides:

\ (m + 12) - 12 = 0 - 12 \
Simplifying this would give us \ m = -12 \: we successfully isolate \(m\).

Remember these tips when using the Subtraction Property of Equality:
  • Subtract the same value from both sides to maintain the balance.
  • Double-check your work by substituting the value back into the original equation to ensure both sides are equal.
Isolating Variables
Isolating the variable is a critical step in solving equations. Isolating a variable means getting it alone on one side of the equation, which tells us its value. In the example \(m - 12 = -12\), we used the Addition Property of Equality to isolate \(m\) by adding 12 to both sides:

\ (m - 12) + 12 = -12 + 12 \
This yielded \ m = 0 \.
Here are some helpful steps for isolating variables:
  • Identify the variable you need to isolate.
  • Determine which operations are affecting the variable.
  • Use the Addition or Subtraction Property of Equality to cancel out these operations on both sides of the equation.
  • Simplify to get the variable alone.
Following these steps will help you solve linear equations effectively.

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