Question

http://prntscr.com/99dfmp

Answer 1

@imqwerty

Answer 2

Step 1-> plot the line \(\large y=-x+25\)

Step 2->consider any point lying on either side of this line
For example say (0,0) and enter these coordinates in the equation \(\large\ y < -x+25\)
If it satisfies the equation then shade the area on the side which includes 0.

Step 3->The boundary of the graph must be dotted and not solid.
Remember that you get a graph with solid boundary only if there is an \(\color{red}{=}\) sign in the equation.
But our equation \(\large y \color{red}{<} -x+25\) has '\(\color{red}{<}\)' so it will be dotted.

Now try to plot it.

Answer 3

http://prntscr.com/99di79

like that?

Answer 4

yes that is the 1st step
an accurate pic for that step is -> http://prntscr.com/99djcv

now try to do the \(Step~2\)

Answer 5

we have to plot this inequality-> \(y <-x+25\)

remember that whenever we plot inequality we get a shaded region

We have already plotted the line \(y=-x+25\) http://prntscr.com/99djcv
Now we need to find out which part to shade

It can be either like this- http://prntscr.com/99dks2
or like this- http://prntscr.com/99dkwi
So we have 2 ways
We know that the points which lie in the correct graph must satisfy the inequality
Now the point lying in the correct shaded region must satisfy the inequality

So lets say that its shaded like this- http://prntscr.com/99dks2

its pretty clear that (0,0) lies in this graph in shaded region
so (0,0) must satisfy the inequality \(\color{blue}{y<-x+25}\)

so we put the coordinates of (0,0) in the inequality to check
we get this-
\(y<-x+25\)
\(0<-(0)+25\)
\(0<25 \) we see that the inequality holds true for (0,0) so it must lie in the graph
and thus this is correct- http://prntscr.com/99dks2

ok till here?

Answer 6

http://prntscr.com/99dnez

is this correct?

Answer 7

yes correct so far
Now the 3rd Step

try to figure it out :)

Answer 8

http://prntscr.com/99drn9

Answer 9

@imqwerty

Answer 10

yes \(\cal\Large\color{green}{Correct!}\)

Answer 11

Tysm.

can u help with part b as well?

Answer 12

@imqwerty

Answer 13

http://prntscr.com/99dt98

Answer 14

okay :)
to check if (1,-2) is a solution you just put these coordinates in our inequality->\(\large y<-x+25\)

if the inequality is satisfied it is a solution.
OR
you can just check if (1,2) lies in the shaded region
If it does it is a solution to the inequality

Answer 15

In this case the solution to the inequality will be all the points which lie under the shaded region.
But the points lying on the dotted line(Boundary) of the graph will not be considered as solutions.

Answer 16

http://prntscr.com/99dwwp

like that?

Answer 17

@imqwerty

Answer 18

yeah (1,2) is a solution and now you have to write the reason and meaning of it being a solution.

Answer 19

The ordered pair is representing the amount of boys and girls which would really be the same out, so we graph it and shade it out.

Answer 20

yes thats ok you can also add that the solution (1,2) follows the given inequality so it holds true.

Answer 21

thnx

Answer 22

np \(\Huge\ddot\smile\)