Problem Description:
The image explains the
Addition Property of Equality and the
Subtraction Property of Equality. These properties are fundamental in solving linear equations. The task is to understand these properties and apply them to solve given examples.
---
Key Concepts:
1.
Addition Property of Equality:
- If \( a = b \), then \( a + c = b + c \).
- This means you can add the same number to both sides of an equation without changing its equality.
2.
Subtraction Property of Equality:
- If \( a = b \), then \( a - c = b - c \).
- This means you can subtract the same number from both sides of an equation without changing its equality.
---
Examples Provided in the Image:
####
Example 1 (Addition Property of Equality):
Solve: \( x - 8 = 9 \)
-
Step 1: Add 8 to both sides of the equation.
\[
x - 8 + 8 = 9 + 8
\]
-
Step 2: Simplify both sides.
\[
x = 17
\]
####
Example 2 (Addition Property of Equality):
Solve: \( x - \frac{1}{2} = \frac{1}{2} \)
-
Step 1: Add \(\frac{1}{2}\) to both sides of the equation.
\[
x - \frac{1}{2} + \frac{1}{2} = \frac{1}{2} + \frac{1}{2}
\]
-
Step 2: Simplify both sides.
\[
x = 1
\]
####
Example 3 (Subtraction Property of Equality):
Solve: \( x + 19 = 28 \)
-
Step 1: Subtract 19 from both sides of the equation.
\[
x + 19 - 19 = 28 - 19
\]
-
Step 2: Simplify both sides.
\[
x = 9
\]
####
Example 4 (Subtraction Property of Equality):
Solve: \( x + 0.5 = 0.75 \)
-
Step 1: Subtract 0.5 from both sides of the equation.
\[
x + 0.5 - 0.5 = 0.75 - 0.5
\]
-
Step 2: Simplify both sides.
\[
x = 0.25
\]
---
Explanation of the Solution:
1.
Addition Property of Equality:
- In the first two examples, the goal is to isolate \( x \) by adding the same number to both sides of the equation. This ensures that the equality remains unchanged.
- For \( x - 8 = 9 \), adding 8 to both sides eliminates the \(-8\) on the left side, leaving \( x \) alone.
- For \( x - \frac{1}{2} = \frac{1}{2} \), adding \(\frac{1}{2}\) to both sides eliminates the \(-\frac{1}{2}\) on the left side.
2.
Subtraction Property of Equality:
- In the last two examples, the goal is to isolate \( x \) by subtracting the same number from both sides of the equation. This ensures that the equality remains unchanged.
- For \( x + 19 = 28 \), subtracting 19 from both sides eliminates the \(+19\) on the left side, leaving \( x \) alone.
- For \( x + 0.5 = 0.75 \), subtracting 0.5 from both sides eliminates the \(+0.5\) on the left side.
---
Final Answer:
The solutions to the examples are:
1. \( x = 17 \)
2. \( x = 1 \)
3. \( x = 9 \)
4. \( x = 0.25 \)
\[
\boxed{x = 17, x = 1, x = 9, x = 0.25}
\]
Parent Tip: Review the logic above to help your child master the concept of properties of equality worksheets.
