Sure! Let's solve the equation [tex]\(0.11 = \frac{2x}{0.2 - x}\)[/tex] step by step.
1. Identify the equation:
[tex]\[
0.11 = \frac{2x}{0.2 - x}
\][/tex]
2. Multiply both sides by [tex]\(0.2 - x\)[/tex] to eliminate the denominator:
[tex]\[
0.11 (0.2 - x) = 2x
\][/tex]
3. Distribute [tex]\(0.11\)[/tex] on the left side:
[tex]\[
0.11 \cdot 0.2 - 0.11x = 2x
\][/tex]
4. Calculate [tex]\(0.11 \cdot 0.2\)[/tex]:
[tex]\[
0.022 - 0.11x = 2x
\][/tex]
5. Rearrange the equation to get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[
0.022 = 2x + 0.11x
\][/tex]
6. Combine like terms on the right side:
[tex]\[
0.022 = 2.11x
\][/tex]
7. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(2.11\)[/tex]:
[tex]\[
x = \frac{0.022}{2.11}
\][/tex]
8. Perform the division:
[tex]\[
x \approx 0.0104265402843602
\][/tex]
So, the solution to the equation [tex]\(0.11 = \frac{2x}{0.2 - x}\)[/tex] is:
[tex]\[
x \approx 0.0104265402843602
\][/tex]
