Answer: x = 3.5
Step-by-step explanation:
<u>Given</u>
x/3 + x/7 = 5/3
<u>Determine the Least Common Multiple (LCM) of the denominators</u>
First 10 multiples of 3: 3, 6, 9, 12, 15, 18, <u>21</u>, 24, 27, 30
First 5 multiples of 7: 7, 14, <u>21</u>, 28, 35
Since 21 is the first overlapping term in both lists, therefore, 21 is the LCM of 3 and 7.
<u>Multiply Least Common Multiple (LCM) of the denominators on both sides</u>
21 (x/3 + x/7) = 21 × 5/3
<u>Expand parentheses and apply the distributive property</u>
7x + 3x = 35
<u>Combine like terms</u>
10x = 35
<u>Divide 10 on both sides</u>
10x / 10 = 35 / 10
![\boxed {x=3.5}](https://tex.z-dn.net/?f=%5Cboxed%20%7Bx%3D3.5%7D)
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