Question

3 a cell phone company offers two texting plans. people who use plan a pay $0.10 for each text sent or received. people who use plan b pay $12 per month, and then pay an additional $0.02 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: Define cost functions

Let $C_A$ be the cost of plan A and $C_B$ be the cost of plan B. For plan A, the cost is $C_A = 0.10x$ (since it's $0.10$ per text and $x$ is the number of texts). For plan B, the cost is $C_B=12 + 0.02x$ (a fixed - cost of $12$ plus $0.02$ per text).

Step2: Write the inequality

We want to find when plan A is cheaper than plan B, so $C_A

Step3: Solve the inequality

Subtract $0.02x$ from both sides:
$0.10x-0.02x<12 + 0.02x-0.02x$
$0.08x<12$
Then divide both sides by $0.08$:
$x<\frac{12}{0.08}$
$x < 150$

Answer:

a. $0.10x<12 + 0.02x$
b. $x < 150$