Question
\( 3 \sqrt[3]{5 y+1}-2=-5 \) The solution set is
Ask by Hammond Gough. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( y = -\frac{2}{5} \).
Solution
We start with the equation:
3∛(5y + 1) - 2 = -5
Step 1: Add 2 to both sides to isolate the cube root term:
3∛(5y + 1) = -5 + 2
3∛(5y + 1) = -3
Step 2: Divide both sides by 3:
∛(5y + 1) = -1
Step 3: Cube both sides to eliminate the cube root:
5y + 1 = (-1)³
5y + 1 = -1
Step 4: Subtract 1 from both sides:
5y = -2
Step 5: Divide by 5:
y = -2/5
Thus, the solution set is { -2/5 }.
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Simplify this solution Extra Insights
To solve the equation \( 3 \sqrt[3]{5y+1} - 2 = -5 \), let's first isolate the cube root. Adding 2 to both sides gives: \[ 3 \sqrt[3]{5y+1} = -3 \] Now, dividing by 3: \[ \sqrt[3]{5y+1} = -1 \] Next, we'll cube both sides: \[ 5y + 1 = (-1)^3 \] \[ 5y + 1 = -1 \] Subtracting 1 from both sides: \[ 5y = -2 \] Finally, dividing by 5: \[ y = -\frac{2}{5} \] So the solution set is \( \left\{ -\frac{2}{5} \right\} \). In conclusion, finding those hidden solutions often requires peeling back equations layer by layer, much like solving a mystery! Keep practicing and you’ll be a math detective in no time!
