Answer :
Let's go through the solution process step by step to identify which step is not part of solving the equation [tex]\(4(3x - 6) = 24\)[/tex].
1. Original Equation:
[tex]\[
4(3x - 6) = 24
\][/tex]
2. Step 1 - Using the distributive property:
[tex]\[
12x - 24 = 24
\][/tex]
* Here, the distributive property is used to multiply 4 with both terms inside the parentheses, so this step is correct and necessary.
3. Step 2 - Adding 24 to both sides:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
* This step involves adding 24 to both sides to help isolate the variable term. This step is correct and part of the solution process.
4. Step 3:
[tex]\[
12x = 48
\][/tex]
* After adding 24 to both sides, the equation simplifies correctly. This step is shown as Step 3.
5. Step 4 - Dividing both sides by 12:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
* Dividing both sides by 12 isolates the variable [tex]\(x\)[/tex]. This is necessary to solve for [tex]\(x\)[/tex].
6. Step 5:
[tex]\[
x = 4
\][/tex]
* The solution for [tex]\(x\)[/tex] is obtained, completing the process.
Now, let’s identify which option is not part of the solution process:
- Option A: Using the distributive property is applied in Step 1, so it is part of the solving process.
- Option C: Dividing both sides by 12 to isolate the variable is applied in Step 4, so it is part of the solving process.
- Option D: Adding 24 to both sides to isolate the variable term is applied in Step 2, so it is part of the solving process.
- Option B: Simplifying by combining variable terms does not occur in the solution process. The equation does not require combining any variable terms, as there is only one variable term. Therefore, Option B is not part of the solution process.
The step that is not part of the solution process is B. Simplifying by combining variable terms.
1. Original Equation:
[tex]\[
4(3x - 6) = 24
\][/tex]
2. Step 1 - Using the distributive property:
[tex]\[
12x - 24 = 24
\][/tex]
* Here, the distributive property is used to multiply 4 with both terms inside the parentheses, so this step is correct and necessary.
3. Step 2 - Adding 24 to both sides:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
* This step involves adding 24 to both sides to help isolate the variable term. This step is correct and part of the solution process.
4. Step 3:
[tex]\[
12x = 48
\][/tex]
* After adding 24 to both sides, the equation simplifies correctly. This step is shown as Step 3.
5. Step 4 - Dividing both sides by 12:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
* Dividing both sides by 12 isolates the variable [tex]\(x\)[/tex]. This is necessary to solve for [tex]\(x\)[/tex].
6. Step 5:
[tex]\[
x = 4
\][/tex]
* The solution for [tex]\(x\)[/tex] is obtained, completing the process.
Now, let’s identify which option is not part of the solution process:
- Option A: Using the distributive property is applied in Step 1, so it is part of the solving process.
- Option C: Dividing both sides by 12 to isolate the variable is applied in Step 4, so it is part of the solving process.
- Option D: Adding 24 to both sides to isolate the variable term is applied in Step 2, so it is part of the solving process.
- Option B: Simplifying by combining variable terms does not occur in the solution process. The equation does not require combining any variable terms, as there is only one variable term. Therefore, Option B is not part of the solution process.
The step that is not part of the solution process is B. Simplifying by combining variable terms.
