Certainly! Let’s solve the problem step by step:
1. Define the fractions: We are given two fractions to sum: [tex]\(\frac{1}{30}\)[/tex] and [tex]\(\frac{1}{70}\)[/tex].
2. Sum the fractions: To sum the fractions, we need to find a common denominator. The denominators are 30 and 70. The least common multiple (LCM) of 30 and 70 is 210. Thus, rewrite each fraction with the common denominator:
[tex]\[
\frac{1}{30} = \frac{7}{210}
\][/tex]
[tex]\[
\frac{1}{70} = \frac{3}{210}
\][/tex]
Now, add the fractions:
[tex]\[
\frac{1}{30} + \frac{1}{70} = \frac{7}{210} + \frac{3}{210} = \frac{7 + 3}{210} = \frac{10}{210} = \frac{1}{21}
\][/tex]
3. Reciprocal of the sum: We are given that the sum of the fractions equals the reciprocal of [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{30} + \frac{1}{70} = \frac{1}{x}
\][/tex]
From the calculation above, we know that:
[tex]\[
\frac{10}{210} = \frac{1}{21}
\][/tex]
Therefore,
[tex]\[
\frac{1}{21} = \frac{1}{x}
\][/tex]
4. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], take the reciprocal of both sides of the equation:
[tex]\[
x = 21
\][/tex]
Hence, the value of [tex]\(x\)[/tex] is 21.
