Under her cell phone plan, Mayerlin pays a flat cost of $55 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Mayerlin can use while staying within her budget.

To solve this problem, we need to set up an inequality that represents Mayerlin's phone bill. The total cost is the sum of a flat cost of $55 per month and an additional $5 per gigabyte for data usage. We want to find how many gigabytes, $ x $, she can use while keeping her total cost under $70.

The inequality can be written as:

\[
55 + 5x < 70
\]

### Solving the inequality:

1. Subtract 55 from both sides:
   \[
   5x < 70 - 55
   \]
   \[
   5x < 15
   \]

2. Divide both sides by 5:
   \[
   x < \frac{15}{5}
   \]
   \[
   x < 3
   \]

### Conclusion:
Mayerlin can use **less than 3 gigabytes** of data to keep her bill under $70 per month.

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Do you want further details or have any questions?

Here are 5 related questions to consider:
1. How would the inequality change if the flat cost increased to $60 per month?
2. What if Mayerlin wanted to keep her bill under $80 per month instead?
3. How would the solution change if each gigabyte cost $7 instead of $5?
4. If Mayerlin’s total data usage exceeded 3 GB, how much would her bill be?
5. How can you express the total cost function $ C(x) $ in terms of $ x $?

**Tip:** Always double-check the direction of the inequality when solving word problems!

Learn how to solve the inequality 55 + 5x < 70 to determine how many gigabytes Mayerlin can use while keeping her cell phone bill under $70 per month. This algebra problem covers solving inequalities and basic algebraic operations. Suitable for students in Grades 6-8.

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