Solving a decimal word problem using a two-step linear Inequality For his phone service, Ali pays a monthly fee of \( \$ 28 \), and he pays an additional \( \$ 0.07 \) per minute of use. The least he has been charged in a month is \( \$ 129.29 \). What are the possible numbers of minutes he has used his phone in a month? Use \( m \) for the number of minutes, and solve your inequality, for \( m \).

To model Ali's phone service charges, we can set up the inequality based on the information given. His total charges can be represented as: \[ 28 + 0.07m \geq 129.29 \] Subtract \( 28 \) from both sides: \[ 0.07m \geq 129.29 - 28 \] \[ 0.07m \geq 101.29 \] Next, divide both sides by \( 0.07 \): \[ m \geq \frac{101.29}{0.07} \] \[ m \geq 1447 \] So, the possible number of minutes Ali has used his phone in a month is \( m \geq 1447 \) minutes. Now, let's dive into some fun facts! Those monthly fees and per-minute charges can trace back to important evolution in phone billing! Back in the day, cellular providers charged by the minute without any cap, which led to wild billing. Now, many plans offer unlimited use or different pricing structures to cater to different needs—making cell plans a math-savvy venture! And speaking of being savvy! When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number. It's an easy mistake to make, but being aware can save you from reaching incorrect conclusions, especially when dealing with dollar amounts or other real-world applications where every cent counts!