To solve the equation [tex]\(6 - 0.2x = 2(6 - 0.6x)\)[/tex], follow these steps:
1. Expand the equation on the right-hand side:
The original equation is:
[tex]\[
6 - 0.2x = 2(6 - 0.6x)
\][/tex]
Distribute the 2 on the right-hand side:
[tex]\[
6 - 0.2x = 2 \cdot 6 - 2 \cdot 0.6x
\][/tex]
Simplify the expression:
[tex]\[
6 - 0.2x = 12 - 1.2x
\][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To eliminate the fraction, let's get all the terms involving [tex]\(x\)[/tex] on one side and the constants on the other side. Add [tex]\(1.2x\)[/tex] to both sides:
[tex]\[
6 - 0.2x + 1.2x = 12 - 1.2x + 1.2x
\][/tex]
[tex]\[
6 + 1.0x = 12
\][/tex]
Combine like terms:
[tex]\[
6 + x = 12
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Subtract 6 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
6 + x - 6 = 12 - 6
\][/tex]
[tex]\[
x = 6
\][/tex]
So, the solution to the equation [tex]\(6 - 0.2x = 2(6 - 0.6x)\)[/tex] is [tex]\(x = 6\)[/tex].
Thus, the correct answer is:
A. [tex]\(x=6\)[/tex]
