Answer :
Sure! Let's go through the steps of solving the equation [tex]\(4(3x - 6) = 24\)[/tex] and identify which option is not part of the solution process.
Original Equation:
[tex]\[ 4(3x - 6) = 24 \][/tex]
Step 1: Using the distributive property
We start by distributing the 4 across the terms inside the parentheses:
[tex]\[ 4 \times 3x - 4 \times 6 = 12x - 24 \][/tex]
This uses the distributive property, so option A is correct.
Step 2: Simplifying by adding 24 to both sides
Add 24 to both sides to eliminate [tex]\(-24\)[/tex] on the left:
[tex]\[ 12x - 24 + 24 = 24 + 24 \][/tex]
[tex]\[ 12x = 48 \][/tex]
This involves adding 24 to both sides, so option B is correct.
Step 3: Isolating the variable by dividing both sides by 12
Divide each side by 12 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{12x}{12} = \frac{48}{12} \][/tex]
[tex]\[ x = 4 \][/tex]
This involves dividing by 12, so option C is correct.
Now, let's look at option D:
Option D: Simplifying by combining variable terms
There were no like terms involving the variables to combine at any step in this process since there was only one [tex]\(12x\)[/tex] term after using the distributive property.
So, the answer is:
D. Simplifying by combining variable terms
This step is not part of the solution process for this particular equation.
Original Equation:
[tex]\[ 4(3x - 6) = 24 \][/tex]
Step 1: Using the distributive property
We start by distributing the 4 across the terms inside the parentheses:
[tex]\[ 4 \times 3x - 4 \times 6 = 12x - 24 \][/tex]
This uses the distributive property, so option A is correct.
Step 2: Simplifying by adding 24 to both sides
Add 24 to both sides to eliminate [tex]\(-24\)[/tex] on the left:
[tex]\[ 12x - 24 + 24 = 24 + 24 \][/tex]
[tex]\[ 12x = 48 \][/tex]
This involves adding 24 to both sides, so option B is correct.
Step 3: Isolating the variable by dividing both sides by 12
Divide each side by 12 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{12x}{12} = \frac{48}{12} \][/tex]
[tex]\[ x = 4 \][/tex]
This involves dividing by 12, so option C is correct.
Now, let's look at option D:
Option D: Simplifying by combining variable terms
There were no like terms involving the variables to combine at any step in this process since there was only one [tex]\(12x\)[/tex] term after using the distributive property.
So, the answer is:
D. Simplifying by combining variable terms
This step is not part of the solution process for this particular equation.
