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Study the steps used to solve the equation.

Given: [tex]\(\frac{c}{2} - 5 = 7\)[/tex]

Step 1: [tex]\(\frac{c}{2} - 5 + 5 = 7 + 5\)[/tex]

Step 2: [tex]\(\frac{c}{2} + 0 = 12\)[/tex]

Step 3: [tex]\(\frac{c}{2} = 12\)[/tex]

Step 4: [tex]\(2\left(\frac{c}{2}\right) = 12(2)\)[/tex]

Step 5: [tex]\(c = 24\)[/tex]

Choose the property that justifies each step of the solution.

Step 1: [tex]\(\square\)[/tex]

Step 2: [tex]\(\square\)[/tex]

Step 3: [tex]\(\square\)[/tex]

Step 4: [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
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
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