Question
Nadeem plans to ride her bike between 12 mi and 15 mi. Write and solve an inequality to model how many hours Nadeem will be riding?
Hint:
If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality. For example, x>5 (x should be greater than 5).
If the symbol is (≥ or ≤) then you fill in the dot and if the symbol is (> or <) then you do not fill in the dot.
The correct answer is: the inequality is 1.2 ≤ t ≤ 1.5.
Given that the speed of the Nadeem is 10 MPH and he rides between 12 mi and 15 mi.
Time = 
Time taken by Nadeem to travel 12 miles = 
h = 1.2 hours
Time taken by Nadeem to travel 15 miles = 
h = 1.5 hours
Time taken by Nadeem to ride between 12 mi and 15 mi is 1.2 to 1.5 hours
If the time taken by Nadeem is represented by t
Then, 1.2 ≤ t ≤ 1.5
Final Answer:
Hence, the inequality is 1.2 ≤ t ≤ 1.5.
Time taken by Nadeem to travel 12 miles =
h = 1.2 hoursTime taken by Nadeem to travel 15 miles =
h = 1.5 hoursTime taken by Nadeem to ride between 12 mi and 15 mi is 1.2 to 1.5 hours
If the time taken by Nadeem is represented by t
Then, 1.2 ≤ t ≤ 1.5
Final Answer:
Hence, the inequality is 1.2 ≤ t ≤ 1.5.
In this question, the time taken to ride by Nadeem is to be calculated with the help of the speed and distance formula (time = distance/speed). So, for example, to determine the time required to complete a journey, we must first know the distance and speed.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Calculating with the time formula gives us the answer as an inequality.
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Step 1: The values on the number line that satisfy each inequality in the compound inequality are shaded on the graph. The graph's endpoint should be marked with a filled-in circle to show that a value included in the inequality symbol is either or; otherwise, the endpoint should be marked with an open circle to show that a value is not included. There should be an arrow pointing in that direction at the end of the graph that never ends.
Step 2: The graph of the compound inequality is the intersection of the two graphs from Step 1 if the compound inequality contains the term AND. Only the portion of the number line that appears in both graphs should be shaded. The graph of the compound inequality is the union of the two graphs from Step 1 if the compound inequality contains the term OR. Incorporate both of these graphs into the last one.
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Solve each compound inequality and graph the solution
On the number line, we can graph the compound inequalities. When graphing compound inequalities, keep the following points in mind.
• Consider a number on the number line that corresponds to the inequality. For example, if x > 2, we must determine where '2' falls on the number line.
• If the inequality is either ">" or "<, "place an open dot (to indicate that the value is "NOT" included).
If the inequality is either "≥" or " ≤, "place a closed dot to include the value.
For example, if x > 2, place an open dot at '2' because the inequality is strict and does not include " =."
• Place an arrow symbol on the right side of the number for the ">" or "≥" sign.
• Place an arrow symbol on the left side of the number for the " <"or " ≤" sign.
• Finally, use the intersection or union, depending on whether "AND" or "OR" is given, to find the final solution.
Solve each compound inequality and graph the solution
On the number line, we can graph the compound inequalities. When graphing compound inequalities, keep the following points in mind.
• Consider a number on the number line that corresponds to the inequality. For example, if x > 2, we must determine where '2' falls on the number line.
• If the inequality is either ">" or "<, "place an open dot (to indicate that the value is "NOT" included).
If the inequality is either "≥" or " ≤, "place a closed dot to include the value.
For example, if x > 2, place an open dot at '2' because the inequality is strict and does not include " =."
• Place an arrow symbol on the right side of the number for the ">" or "≥" sign.
• Place an arrow symbol on the left side of the number for the " <"or " ≤" sign.
• Finally, use the intersection or union, depending on whether "AND" or "OR" is given, to find the final solution.
