Question
Solve. \[ \begin{array}{l}\sqrt[3]{5 x-3}=-2 \\ \text { A. The solution(s) is/are the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) } \\ \text { B. There is no solution. }\end{array} \text { ? } \]
Ask by Schmidt Mccarthy. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( x = -1 \).
Solution
We are given the equation:
∛(5x − 3) = −2
To eliminate the cube root, cube both sides of the equation:
(∛(5x − 3))³ = (−2)³
This simplifies to:
5x − 3 = −8
Next, solve for x by adding 3 to both sides:
5x = −8 + 3
5x = −5
Divide both sides by 5:
x = −5/5
x = −1
Thus, the solution is x = −1.
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Simplify this solution Beyond the Answer
To solve the equation \(\sqrt[3]{5x-3}=-2\), we first cube both sides to eliminate the cube root: \[ 5x - 3 = (-2)^3 \] Calculating the right side gives us: \[ 5x - 3 = -8 \] Next, we add 3 to both sides: \[ 5x = -8 + 3 \] \[ 5x = -5 \] Now, divide both sides by 5: \[ x = -1 \] So, the solution is \(x = -1\). In response to the choices presented: **A. The solution(s) is/are -1.** There's no need for choice B since we found a valid solution!
