Inequalities and Real-World Constraints Mastery Quiz

The inequality x > 5 means that x is greater than 5 and does not include the value 5 itself, like the requirement for a minimum height to ride a roller coaster. The inequality x ≥ 5 means that x is greater than or equal to 5, including the value 5, like the requirement for a minimum age of 5 years to enter kindergarten.

In a marathon, the maximum time allowed to complete the race is 20 minutes. This can be represented by the inequality x < 20, where x represents the time in minutes to complete the race. Any time less than 20 minutes satisfies the condition.

To represent the solution set of x ≥ 3 on a number line diagram, a closed circle is placed on the point 3, indicating that 3 is included in the solution set. Then, a line extends to the right, representing all numbers greater than or equal to 3. This method visually demonstrates that the inequality x ≥ 3 includes 3 and all numbers greater than 3, as represented on the number line.

<p>An example of a real-world problem that can be represented using the inequality x &lt; 3 is the maximum height a ball reaches when thrown upward with an initial velocity. The inequality x &lt; 3 represents the constraint that the height of the ball is less than 3 meters at any given time during its flight.</p> Signup and view all the answers

<p>The solution set for the inequality x &gt; 4 on a number line diagram is represented by an open circle at the number 4, indicating that 4 is not included in the solution set, and an arrow extending towards positive infinity, indicating that all numbers greater than 4 are included in the solution set.</p> Signup and view all the answers

<p>A mathematical problem that can be represented using the inequality x ≥ 7 is the minimum temperature required for a chemical reaction to occur. The inequality x ≥ 7 represents the constraint that the temperature must be 7 degrees or higher for the reaction to take place.</p> Signup and view all the answers