Question
Solve. Clear fractions or decimals first. \[ \frac{2}{5}+\frac{1}{3} t=\frac{1}{5} \]
Ask by Willis Mccoy. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( t = -\frac{3}{5} \)
Solution
To solve the equation (2/5) + (1/3)t = (1/5), we'll first clear the fractions. The denominators are 5 and 3, and their least common denominator is 15. Multiply every term by 15:
15*(2/5) + 15*(1/3)t = 15*(1/5)
This simplifies to:
6 + 5t = 3
Subtract 6 from both sides:
5t = 3 − 6
5t = −3
Finally, divide both sides by 5:
t = −3/5
The solution is t = −3/5.
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Simplify this solution Bonus Knowledge
To solve the equation, let's clear the fractions by finding a common denominator. The least common multiple of the denominators 5 and 3 is 15. We can multiply every term in the equation by 15 to eliminate the fractions: \[ 15 \left( \frac{2}{5} \right) + 15 \left( \frac{1}{3} t \right) = 15 \left( \frac{1}{5} \right) \] This simplifies to: \[ 6 + 5t = 3 \] Next, we can isolate \( t \) by subtracting 6 from both sides: \[ 5t = 3 - 6 \] \[ 5t = -3 \] Now, divide by 5 to solve for \( t \): \[ t = -\frac{3}{5} \] Thus, the solution to the equation is: \[ t = -\frac{3}{5} \]
