Question
Solve the equation and check the solution. \( 10 \mathrm{t}=-26 \) The solution set is \( \{\square\} \). (Type an integer or a simplified fraction.)
Ask by Hammond Maxwell. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( t = -\frac{13}{5} \).
Solution
1. The given equation is
\[
10t = -26.
\]
2. To solve for \( t \), divide both sides by 10:
\[
t = \frac{-26}{10}.
\]
3. Simplify the fraction by dividing numerator and denominator by 2:
\[
t = \frac{-13}{5}.
\]
4. To check the solution, substitute \( t = \frac{-13}{5} \) back into the original equation:
\[
10\left(\frac{-13}{5}\right) = \frac{10 \times (-13)}{5} = \frac{-130}{5} = -26.
\]
Since the left-hand side equals the right-hand side, the solution is correct.
The solution set is \( \left\{ -\frac{13}{5} \right\} \).
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Simplify this solution Extra Insights
To solve the equation \( 10t = -26 \), we can isolate \( t \) by dividing both sides by \( 10 \). \[ t = \frac{-26}{10} = \frac{-13}{5} \] Now, we will check the solution by substituting \( t \) back into the original equation: \[ 10 \left(\frac{-13}{5}\right) = -26 \] Calculating the left-hand side: \[ 10 \cdot \frac{-13}{5} = \frac{-130}{5} = -26 \] Since both sides are equal, the solution is verified. Thus, the solution set is \( \left\{ \frac{-13}{5} \right\} \).
