Certainly! Let's go through the steps and identify the mathematical properties that justify each one.
Given equation:
[tex]\[ \frac{c}{2} - 5 = 7 \][/tex]
### Step-by-Step Solution:
Step 1:
[tex]\[ \frac{c}{2} - 5 + 5 = 7 + 5 \][/tex]
- Property: Addition Property of Equality (Adding the same number to both sides of the equation to maintain equality)
Step 2:
[tex]\[ \frac{c}{2} + 0 = 12 \][/tex]
- Property: Additive Identity (Adding 0 does not change the value, recognizing that [tex]\(-5 + 5 = 0\)[/tex])
Step 3:
[tex]\[ \frac{c}{2} = 12 \][/tex]
- Property: Simplification (Simplifying the equation by removing the 0 from the left side)
Step 4:
[tex]\[ 2 \left(\frac{c}{2}\right) = 12 \times 2 \][/tex]
- Property: Multiplicative Property of Equality (Multiplying both sides of the equation by 2 to isolate [tex]\(c\)[/tex])
### Summary of Properties for Each Step:
- Step 1: Addition Property of Equality
- Step 2: Additive Identity
- Step 3: Simplification
- Step 4: Multiplicative Property of Equality
Thus, the properties justifying the steps are as follows:
1. Step 1: Addition Property of Equality
2. Step 2: Additive Identity
3. Step 3: Simplification
4. Step 4: Multiplicative Property of Equality
