Questions: Solve the following inequality. [ 5(x^2-1)>24 x ] Select the correct choice below and, if necessary, fill in the answer box. A. The solution set is . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no real solution.

Solve the following inequality. [ 5(x^2-1)>24 x ] Select the correct choice below and, if necessary, fill in the answer box. A. The solution set is . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no real solution.
Transcript text: Solve the following inequality. \[ 5\left(x^{2}-1\right)>24 x \] Select the correct choice below and, if necessary, fill in the answer box. A. The solution set is $\square$ . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no real solutionon.
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Solution

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Solution Steps

Step 1: Move all terms to one side (if not already done)

Given inequality: $5 x^{2} - 24 x - 5 > 0$

Step 2: Factor the function (if possible)

Factored form: $\left(x - 5\right) \left(5 x + 1\right)$

Step 3: Find the roots

Roots: $\left\{- \frac{1}{5}, 5\right\}$

Step 4: Determine intervals and test points
Step 5: Solve the inequality

For $>$, we include intervals where $f(x) > 0$.

Final Answer:

Solutions: $\left(-\infty, - \frac{1}{5}\right) \cup \left(5, \infty\right)$, rounded to 2 decimal places.

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