Solve the following inequality and check for extraneous solutions.
$\sqrt{5 x - 4} < 3 x - 7$
Choose the appropriate answer and fill in the values. Round your answer to three decimal places.
$x <$
$x >$
$< x \leq$
$\leq x <$

Answer

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Answer

$The inequality \sqrt{5 x - 4} < 3 x - 7 has no solution.$

Steps

Step 1 ：Start by squaring both sides of the inequality to eliminate the square root. Be cautious as this can sometimes introduce extraneous solutions.

Step 2 ：Simplify the equation and solve for x.

Step 3 ：The solutions obtained are $x = \frac{47}{18} - \frac{\sqrt{301}}{18}$ and $x = \frac{\sqrt{301}}{18} + \frac{47}{18}$ .

Step 4 ：Check for extraneous solutions by substituting the solutions back into the original inequality.

Step 5 ：Neither of the solutions are valid when substituted back into the original inequality.

Step 6 ： $The inequality \sqrt{5 x - 4} < 3 x - 7 has no solution.$

Solve the following inequality and check for extraneous solutions.5x−4<3x−7Choose the appropriate answer and fill in the values. Round your answer to three decimal places.x<x><x≤≤x<

Answer

Popular Problems

Solve the following inequality and check for extraneous solutions.
$\sqrt{5 x - 4} < 3 x - 7$
Choose the appropriate answer and fill in the values. Round your answer to three decimal places.
$x <$
$x >$
$< x \leq$
$\leq x <$