Answer :
To solve the equation [tex]\(4(3x - 6) = 24\)[/tex], let's go through each step and understand what is happening:
1. Original Equation:
[tex]\[
4(3x - 6) = 24
\][/tex]
This is the initial equation we start with.
2. Step 1: Distribute the 4
[tex]\[
12x - 24 = 24
\][/tex]
Here, the 4 is distributed to both terms inside the parentheses, [tex]\(3x\)[/tex] and [tex]\(-6\)[/tex]. This results in [tex]\(12x - 24\)[/tex].
3. Step 2: Add 24 to both sides
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
To isolate the term with the variable [tex]\(x\)[/tex], we add 24 to both sides, effectively cancelling out the [tex]\(-24\)[/tex] on the left side.
4. Step 3: Simplify the equation
[tex]\[
12x = 48
\][/tex]
After adding 24 to both sides, we are left with [tex]\(12x\)[/tex] on the left and 48 on the right.
5. Step 4: Divide both sides by 12
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
To solve for [tex]\(x\)[/tex], divide both sides of the equation by 12, which is the coefficient of [tex]\(x\)[/tex].
6. Step 5: Simplify to find the value of [tex]\(x\)[/tex]
[tex]\[
x = 4
\][/tex]
This is the resulting value after dividing both sides.
Each of these steps logically follows from the previous one as part of the solution process for the equation. Therefore, all the steps provided in the solution are indeed part of the process. There isn't a step present that doesn't belong in solving the equation as described. As such, each step contributes to the solution, and none is extraneous or incorrect.
1. Original Equation:
[tex]\[
4(3x - 6) = 24
\][/tex]
This is the initial equation we start with.
2. Step 1: Distribute the 4
[tex]\[
12x - 24 = 24
\][/tex]
Here, the 4 is distributed to both terms inside the parentheses, [tex]\(3x\)[/tex] and [tex]\(-6\)[/tex]. This results in [tex]\(12x - 24\)[/tex].
3. Step 2: Add 24 to both sides
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
To isolate the term with the variable [tex]\(x\)[/tex], we add 24 to both sides, effectively cancelling out the [tex]\(-24\)[/tex] on the left side.
4. Step 3: Simplify the equation
[tex]\[
12x = 48
\][/tex]
After adding 24 to both sides, we are left with [tex]\(12x\)[/tex] on the left and 48 on the right.
5. Step 4: Divide both sides by 12
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
To solve for [tex]\(x\)[/tex], divide both sides of the equation by 12, which is the coefficient of [tex]\(x\)[/tex].
6. Step 5: Simplify to find the value of [tex]\(x\)[/tex]
[tex]\[
x = 4
\][/tex]
This is the resulting value after dividing both sides.
Each of these steps logically follows from the previous one as part of the solution process for the equation. Therefore, all the steps provided in the solution are indeed part of the process. There isn't a step present that doesn't belong in solving the equation as described. As such, each step contributes to the solution, and none is extraneous or incorrect.
