Sure, let's go through the steps to solve the equation [tex]\(4x - 12 = 20\)[/tex] in detail and understand how Step 3 helps in solving the equation.
1. Original Equation: [tex]\(4x - 12 = 20\)[/tex]
2. Step 1: Add 12 to both sides.
To eliminate the constant term [tex]\(-12\)[/tex] from the left side of the equation, we add 12 to both sides:
[tex]\[
4x - 12 + 12 = 20 + 12
\][/tex]
Simplifying both sides, we get:
[tex]\[
4x = 32
\][/tex]
3. Step 2: Divide both sides by 4.
To isolate the variable [tex]\(x\)[/tex], we divide both sides of the equation by the coefficient of [tex]\(x\)[/tex], which is 4:
[tex]\[
\frac{4x}{4} = \frac{32}{4}
\][/tex]
Simplifying both sides, we get:
[tex]\[
x = 8
\][/tex]
4. Step 3: Solution.
The variable [tex]\(x\)[/tex] has been isolated and the solution to the equation is [tex]\(x = 8\)[/tex].
So, in Step 3 of the explained solution, dividing both sides of the equation by 4 is crucial as it helps isolate the variable [tex]\(x\)[/tex]. By dividing 4x by 4, we are left with [tex]\(x\)[/tex] alone on the left side, and by dividing 32 by 4, we simplify the constant on the right side to 8. This step leads us directly to the solution.
Therefore, the correct answer is:
A. Dividing both sides by 4 isolates the variable.
