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
