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.

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!

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be