Problem 15 - College Algebra and Calculus: An Applied Approach

Question

Determine whether each value of \(x\) is a solution of the equation. Equation $$ \sqrt{2 x-3}=3 $$ Values (a) \(x=6\) (b) \(x=-3\) (c) \(x=-\frac{1}{3}\) (d) \(x=-2\)

Step-by-Step Solution

Answer

The solutions to the inequality \(5x - 12 > 0\) are \(x = 3\) and \(x = \frac{5}{2}\).

Step 1: Checking x = 3

If you plug in \(x = 3\) into the inequality, it becomes \(5*3 - 12\), which equals \(3\). Since 3 > 0, \(x = 3\) is a solution.

Step 2: Checking x = -3

When you insert \(x = -3\) into the inequality, it becomes \(5*(-3) - 12\), which equals \(-27\). Because -27 is not greater than 0, \(x = -3\) is not a solution.

Step 3: Checking x = 5/2

Plugging in \(x = \frac{5}{2}\) into the inequality gives \(5*\frac{5}{2} - 12\), which equals \(\frac{1}{2}\). As this is greater than 0, \(x = \frac{5}{2}\) is a solution.

Step 4: Checking x = 3/2

Finally, replacing \(x\) with \(\frac{3}{2}\) results in the expression \(5*\frac{3}{2} - 12\), which equals \(-3\). As this is not greater than 0, \(\frac{3}{2}\) is not a solution.