You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per minute. The second plan charges a monthly fee of $\$ 29.95$ plus 8 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? minutes Question Help: $\square$ Video $D$ Post to forum Submit Question

Step 1 ：Let's denote the number of minutes you use in a month as \(x\).

Step 2 ：For the first plan, the cost is \(0.23x\) dollars.

Step 3 ：For the second plan, the cost is \(29.95 + 0.08x\) dollars.

Step 4 ：The second plan is preferable when it costs less than the first plan, so we set up the inequality: \(29.95 + 0.08x < 0.23x\).

Step 5 ：Subtract \(0.08x\) from both sides to get: \(29.95 < 0.15x\).

Step 6 ：Then divide both sides by \(0.15\) to solve for \(x\): \(x > 29.95 / 0.15\).

Step 7 ：Calculate the right side: \(x > 199.67\).

Step 8 ：Since the number of minutes cannot be a fraction, we round up to the nearest whole number.

Step 9 ：\(\boxed{x > 200}\) is the final answer, meaning you would have to use at least 200 minutes in a month for the second plan to be preferable.