Question

1. a cell phone company offers two texting plans. people who use plan a pay 10 cents for each text sent or received. people who use plan b pay 12 dollars per month, and then pay an additional 2 cents for each text sent or received.

a. write an inequality to represent the fact that it is cheaper for someone to use plan a than plan b. use x to represent the number of texts they send.
b. solve the inequality.

Explanation:

Step1: Write cost expressions for each plan

Plan A cost: \(10x\) cents (since 10 cents per text). Plan B cost: \(1200 + 2x\) cents (12 dollars = 1200 cents plus 2 cents per text).

Step2: Set up the inequality

Since plan A is cheaper than plan B, \(10x<1200 + 2x\).

Step3: Solve the inequality

Subtract \(2x\) from both sides: \(10x-2x<1200+2x - 2x\), so \(8x<1200\).
Divide both sides by 8: \(x < \frac{1200}{8}\), so \(x<150\).

Answer:

a. The inequality is \(10x<1200 + 2x\).
b. The solution of the inequality is \(x < 150\).