Answered

Fill in the missing property for Reason 2.

Statement | Reason
---|---
1) [tex]\(-12x - 3 = -3x + 19\)[/tex] | 1) Given
2) [tex]\(-12x = -3x + 22\)[/tex] | 2) Addition Property of Equality
3) [tex]\(-9x = 22\)[/tex] | 3) Subtraction Property of Equality
4) [tex]\(x = -\frac{22}{9}\)[/tex] | 4) Division Property of Equality

Options:
- Addition Property of Equality
- Subtraction Property of Equality
- Symmetric Property
- Substitution Property



Answer :

GinnyAnswer
Let's go through the problem step-by-step to fill in the missing properties and complete the solution.

1. Given Equation:
[tex]\[ -12x - 3 = -3x + 19 \][/tex]

2. Apply Addition Property of Equality to move terms involving [tex]\( x \)[/tex] to one side:
[tex]\[ -12x - 3 + 3 = -3x + 19 + 3 \][/tex]
Simplifying, we get:
[tex]\[ -12x = -3x + 22 \][/tex]

3. Apply Subtraction Property of Equality to isolate terms involving [tex]\( x \)[/tex]:
Subtract [tex]\(-3x\)[/tex] from both sides:
[tex]\[ -12x + 3x = -3x + 3x + 22 \][/tex]
Simplifying, we get:
[tex]\[ -9x = 22 \][/tex]

4. Apply Division Property of Equality to solve for [tex]\( x \)[/tex]:
Divide both sides by [tex]\(-9\)[/tex]:
[tex]\[ x = \frac{22}{-9} \][/tex]
Simplifying, we get:
[tex]\[ x = -\frac{22}{9} \][/tex]

Now, filling in the reasons:

1. Statement:
[tex]\[ -12x - 3 = -3x + 19 \][/tex]
Reason: Given

2. Statement:
[tex]\[ -12x = -3x + 22 \][/tex]
Reason: Addition Property of Equality

3. Statement:
[tex]\[ -9x = 22 \][/tex]
Reason: Subtraction Property of Equality

4. Statement:
[tex]\[ x = -\frac{22}{9} \][/tex]
Reason: Division Property of Equality

Thus, the completed solution with reasons is:

1. Statement: [tex]\(-12x - 3 = -3x + 19\)[/tex]
Reason: Given

2. Statement: [tex]\(-12x = -3x + 22\)[/tex]
Reason: Addition Property of Equality

3. Statement: [tex]\(-9x = 22\)[/tex]
Reason: Subtraction Property of Equality

4. Statement: [tex]\( x = -\frac{22}{9} \)[/tex]
Reason: Division Property of Equality

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