Question

writing and solving linear inequalities
sal is trying to determine which cell - phone and service plan to buy for his mother. the first phone costs $100 and $55 per month for unlimited usage. the second phone costs $150 and $51 per month for unlimited usage. how many months will it take for the second phone to be less expensive than the first phone?
the inequality that will determine the number of months, x, that are required for the second phone to be less expensive is 100 + 55x>150 + 51x.
the solution to the inequality is x > 12.5.
sals mother would have to keep the second cell - phone plan for at least 13 months in order for it to be less expensive.

Explanation:

Step1: Set up the inequality

Let $x$ be the number of months. The cost of the first - phone is $100 + 55x$ and the cost of the second phone is $150+51x$. We want to find when the second phone is less expensive than the first, so the inequality is $100 + 55x>150 + 51x$.

Step2: Solve the inequality

Subtract $51x$ from both sides: $100 + 55x-51x>150 + 51x-51x$, which simplifies to $100 + 4x>150$. Then subtract 100 from both sides: $100-100 + 4x>150 - 100$, getting $4x>50$. Divide both sides by 4: $x>\frac{50}{4}=12.5$.

Step3: Determine the number of months

Since the number of months $x$ must be a whole number and $x>12.5$, the smallest whole - number value of $x$ is 13.

Answer:

13