It is given that speech can be 15 minutes, or within that time by 4 minutes.
This means that the speech time can vary around 15 minutes by 4 more or less minutes.
So the limits of speech times are:
Upper limit = 15 + 4 = 19 minutes
Lower limit = 15 - 4 = 11 minutes
So, to find out which absolute value equation represents these limits, we have to solve each absolute value equation.
1st equation:
[tex]\begin{gathered} |t+15|=4 \\ t+15=\pm4 \\ t+15=4,t+15=-4 \\ t=4-15,t=-4-15 \\ t=-11,t=-19 \end{gathered}[/tex]As you can see, these are not the limits we want since they are negative.
So 1st equation is incorrect.
2nd equation:
[tex]\begin{gathered} |t-4|=15 \\ t-4=\pm15 \\ t-4=15,t-4=-15 \\ t=15+4,t=-15+4 \\ t=19,t=-11 \end{gathered}[/tex]As you can see, these are not limits we want since 11 is negative.
So 2nd equation is also incorrect.
3rd equation:
[tex]\begin{gathered} |t-15|=4 \\ t-15=\pm4 \\ t-15=4,t-15=-4 \\ t=4+15,t=-4+15 \\ t=19,t=11 \end{gathered}[/tex]Finally, we got the exact same limits that we wanted t = 19 minutes and t = 11 minutes
Therefore, the correct absolute value equation is the 3rd equation.