Q:

Can someone check if I have the right answers? Sorry for the bad quality. ​Also, how do I change the amount of points? It says ten points but when I submit the question it gives five points.

Accepted Solution

A:
Answer:3. a ≤ 7, a > 3; <-------------7 - - - - - - - 3------------->4. d ≤ 10, d < 9; <-----------------------10---9- - - - - - - - - ->5. 8t ≤ 360, t ≤45Step-by-step explanation:3. 6a ≤ 42 < divide both sides by 6 to get a by itselfa ≤ 7 < this is correcta + 4 > 7 < subtract 4 from both sides to isolate aa > 3 this is also correct!now to graph these inequalities on the number line, we will do them one at a timea ≤ 7, you would put a closed circle (or a bracket) on 7, as the answer is included in the solution, and you would shade to the left of 7, as a has to be less than or equal to 7 in order for the inequality to be true< ----------7 - - - - >now for a > 3,you would shade numbers to the right of 3, as a has to be greater than 3 in order for the inequality to be true. you would put an open circle (or a parentheses) on the number 3, as its not included in the solution as shown by the inequality symbol< - - - - 3--------->together on a number line, both inequalities would look like the following:<-------------7 - - - - - - - 3------------->the middle section is not included in either of the inequalities4. d - 8 ≤ 2 < add 8 to both sidesd ≤ 10 < in your original answer, you forgot to add 8 to the right side of the equation, remember that whatever you do to the left you also do to the right sideon a number line, we would shade to the left of 10, as any answer for d would have to be less than or equal to 10 in order for the inequality to be true. again, a closed circle (or bracket) would be on the number 10 as it is included in the solution< ----------10 - - - - >9d < 81 <-- divide both sides by 9 to get d aloned < 9 < this is correct in your original answeron a number line, we would shade to the left of 9, as any number inserted into the inequality for d has to be less than 9 in order for the inequality to be true. we would put an open circle (or parentheses) on the number 9 because it is not included in the solution< ----------9 - - - - >together on a number line, both terms would look like this:<-----------------------10---9- - - - - - - - - ->since both are being shaded to the left, both would have a line going to the left5. banquet room holds 360 people, with 8 people per table (t)8t ≤ 360 < this is the correct inequality, as we cannot exceed 360 people in the room, and we can seat 8 people at each tablenow we divide both sides by 8 in the inequality to get t alonet ≤ 45so there can only be 45 tables or less in the entire banquet in order to not exceed the 360 person capacityon a number line the inequality looks like the following:< --------45 - - - >45 is included in the solution as we can have 45 tables for 8 people each, and we would be at max capacity in the banquet. 45 on the number line would have a closed circle (or bracket) on the number itselfhope this helped!