Question

Complete the table with three expressions in words and the corresponding expression using mathematic symbols. Use all four inequality symbols:.Expression Mathematical expressionMax Speed limit is 65=65Part 2Travel back in time to the year 2008, when text messages were charged per text. Some carriers charged $59 for a basic text package of 200 texts and 20 cents per text after that. Today, most packages include unlimited text and data but cost closer to $100 a month.Write and solve an equation to determine the range of text messages you can send with the 2008 plan without spending more than $100.If you have a phone, look at your data summary. Is this range your average daily number, weekly number, or monthly number of texts? Determine how much you would have paid for the month if you had the 2008 text plan? Write this as an equation and solve it.Part 3Find another real-life situation that can be written as an inequality in one variable. Explain the situation, write the equation and then solve it.

Answer 1

The maximum number of additional texts one can send under the 2008 plan without spending more than $100 is 205, leading to a total of 405 texts sent. An example of real-life inequality is budgeting for entertainment, where watching not more than 4 movies a month keeps the expense within a $50 budget.

Step-by-step explanation:

Part 2: Calculating the Text Message Plan Costs

In 2008, a cell phone carrier charged $59 for a basic text package of 200 texts and an additional $0.20 per text after the 200-text limit. To find out how many text messages can be sent without spending more than $100, we can set up an inequality.

Let x represent the number of texts sent beyond the initial 200.
Then the total cost is $59 + $0.20x. We want this total to be less than or equal to $100:

$59 + $0.20x ≤ $100

To find the value of x, we subtract $59 from both sides of the inequality:

$0.20x ≤ $41

Then we divide both sides by $0.20 to find the number of additional texts:

x ≤ 205

So, you can send up to 205 additional texts, for a total of 405 texts, without exceeding $100.

Part 3: Real-Life Inequality Situation

An example of a real-life situation involving inequality is budgeting for entertainment. Suppose you have a budget of $50 for entertainment each month and movies cost $12 per ticket.

Let y be the number of movies you can watch each month. The inequality is:

$12y ≤ $50

To solve for y, divide both sides by $12:

y ≤ 4.1667

Since you can't watch a fraction of a movie at the theater, you can watch at most 4 movies per month without exceeding your budget.