Sure! Let's solve the given problems step-by-step.
### 1. Solving the equation [tex]\(2 - x = x\)[/tex]
1. Given the equation:
[tex]\[
2 - x = x
\][/tex]
2. To isolate [tex]\(x\)[/tex], we first add [tex]\(x\)[/tex] to both sides of the equation:
[tex]\[
2 = x + x
\][/tex]
3. Simplify the right-hand side:
[tex]\[
2 = 2x
\][/tex]
4. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{2}{2}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 1
\][/tex]
So, [tex]\(x = 1\)[/tex].
### 2. Solving the expression [tex]\(\frac{3^3 \times 10^5 \times 25}{5 \times 65}\)[/tex]
1. Calculate each component of the expression:
- [tex]\(3^3 = 27\)[/tex]
- [tex]\(10^5 = 100,000\)[/tex]
- [tex]\(25 = 25\)[/tex] (since it is already in its simplest form)
- [tex]\(5 \times 65 = 325\)[/tex]
2. Compute the numerator:
[tex]\[
27 \times 100,000 \times 25
\][/tex]
- First, multiply 27 by 100,000:
[tex]\[
27 \times 100,000 = 2,700,000
\][/tex]
- Then multiply the result by 25:
[tex]\[
2,700,000 \times 25 = 67,500,000
\][/tex]
3. Now, divide the numerator by the denominator:
[tex]\[
\frac{67,500,000}{325}
\][/tex]
4. Perform the division:
[tex]\[
\frac{67,500,000}{325} = 207,692.3076923077
\][/tex]
Thus, the result of the expression [tex]\(\frac{3^3 \times 10^5 \times 25}{5 \times 65}\)[/tex] is approximately [tex]\(207,692.3076923077\)[/tex].
### Summary:
- The solution to the equation [tex]\(2 - x = x\)[/tex] is:
[tex]\[
x = 1
\][/tex]
- The value of the expression [tex]\(\frac{3^3 \times 10^5 \times 25}{5 \times 65}\)[/tex] is:
[tex]\[
207,692.3076923077
\][/tex]
