To solve for [tex]\( x \)[/tex] in the equation [tex]\( 5x = \frac{10}{11} \)[/tex], we need to isolate [tex]\( x \)[/tex]. Here's the step-by-step process:
1. Start with the given equation:
[tex]\[
5x = \frac{10}{11}
\][/tex]
2. To isolate [tex]\( x \)[/tex], we need to divide both sides of the equation by 5. This can be written as:
[tex]\[
x = \frac{\frac{10}{11}}{5}
\][/tex]
3. Dividing by 5 is the same as multiplying by its reciprocal, which is [tex]\( \frac{1}{5} \)[/tex]. So we rewrite the equation as:
[tex]\[
x = \frac{10}{11} \times \frac{1}{5}
\][/tex]
4. Now, multiply the fractions:
[tex]\[
x = \frac{10 \times 1}{11 \times 5} = \frac{10}{55}
\][/tex]
5. Simplify the fraction [tex]\( \frac{10}{55} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
x = \frac{10 \div 5}{55 \div 5} = \frac{2}{11}
\][/tex]
So, the solution to the equation [tex]\( 5x = \frac{10}{11} \)[/tex] is [tex]\( x = \frac{2}{11} \)[/tex].
The correct answer is (4) [tex]\( x = \frac{2}{11} \)[/tex].
