In Exercises 53-62, some applications of inequalities are...

In Exercises $53-62,$ some applications of inequalities are shown. A busy person glances at a digital clock that shows $9: 36 .$ Another glance a short time later shows the clock at $9: 44 .$ Express the amount of time $t$ (in min) that could have elapsed between glances by use of inequalities. Graph these values of $t$.

In Exercises $53-62,$ some applications of inequalities are shown.
A busy person glances at a digital clock that shows $9: 36 .$ Another glance a short time later shows the clock at $9: 44 .$ Express the amount of time $t$ (in min) that could have elapsed between glances by use of inequalities. Graph these values of $t$.

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Key Concepts

Graphing Inequalities

Graphing inequalities means displaying the solution set of an inequality on a number line or coordinate system. This visual method helps in understanding the range of valid values, and in this context, it allows one to see the span of possible elapsed time values.

Time Measurement and Intervals

The concept of time measurement and intervals is important in understanding how to quantify the duration between events. Recognizing time as a continuous variable and correctly expressing that interval in minutes is key to setting up the proper inequality model.

Inequalities

Inequalities involve mathematical expressions that use symbols such as <, ?, >, or ? to compare two quantities. They are used to determine a range of possible values for a variable instead of an exact value, which is essential in modeling situations where there is a range of feasible outcomes.

Translating Real-World Situations into Mathematical Models

This concept involves interpreting a real-life scenario—in this case, the elapsed time between two events—and representing it mathematically using inequalities. This translation forms the bridge between practical problems and their abstract mathematical solutions.

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