What is the value of s in the equation 1/2 + 2/5s = s - 3/4?

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In summary, the conversation involved solving an equation on Khan Academy and someone asking for help understanding a specific step. They were advised to multiply by the least common multiple of the denominators to clear them away and make the equation easier to solve. The final answer was found to be s = 25/12.
  • #1
EngineerJay
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Hey everyone was having trouble solving this on Khan academy. The way they got the answer made no sense what so ever so hoping anyone here can help.

If 1/2 + 2/5s = s - 3/4, what is the value of s?
 
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  • #2
EngineerJay said:
[tex]
\text{Solve for }s:\;\;\tfrac{1}{2} + \tfrac{2}{5}s \;=\; s - \tfrac{3}{4}[/tex]

[tex]\begin{array}{ccc}\text{Multiply by 20:} & 10 + 8s \;=\;20s - 15 \\
\text{Simplify:} & 12s \;=\;25 \\
\text{Therefore:} & s \;=\;\frac{25}{12}
\end{array}[/tex]
 
  • #3
Okay so why did you multiply by 20? And how exactly?
 
  • #4
Since 20 is the least common multiple of 2, 4 and 5, multiplying by 20 clears away the denominators of the fractions, like this:

$$\dfrac12 + \dfrac{2}{5}s = s - \dfrac34$$

Multiply each side by 20:

$$20\left(\dfrac12 + \dfrac{2}{5}s\right) = 20\left(s - \dfrac34\right)$$

Expand:

$$20\cdot\dfrac12 + 20\cdot\dfrac{2}{5}s = 20s - 20\cdot\dfrac34$$

Evaluate:

$$10+8s=20s-15\implies s=\dfrac{25}{12}$$
 
  • #5
Wow thanks for the help! Now that I know I should of found the lcm of 2, 4 and 5 I feel some type of way(Giggle)! Again Thank you.
 

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