Question

Can someone check if I have the right answers?

Answer 1

Answer:

3. a ≤ 7, a > 3; <-------------7 - - - - - - - 3------------->

4. d ≤ 10, d < 9; <-----------------------10---9- - - - - - - - - ->

5. 8t ≤ 360, t ≤45

Step-by-step explanation:

3. 6a ≤ 42 < divide both sides by 6 to get a by itself

a ≤ 7 < this is correct

a + 4 > 7 < subtract 4 from both sides to isolate a

a > 3 this is also correct!

now to graph these inequalities on the number line, we will do them one at a time

a ≤ 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 inequalities

4. d - 8 ≤ 2 < add 8 to both sides

d ≤ 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 side

on 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 alone

d < 9 < this is correct in your original answer

on 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 left

5. 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 table

now we divide both sides by 8 in the inequality to get t alone

t ≤ 45

so there can only be 45 tables or less in the entire banquet in order to not exceed the 360 person capacity

on 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 itself

hope this helped!