Mustafa, heloise, and gia have written more than a combined total of articles for the school newspaper. heloise has written \dfrac{1}{4}
4
1
start fraction, 1, divided by, 4, end fraction as many articles as mustafa has. gia has written \dfrac{3}{2}
2
3
start fraction, 3, divided by, 2, end fraction as many articles as mustafa has.
write an inequality to determine the number of articles, mmm, mustafa could have written for the school newspaper.
what is the solution set of the inequality?

Step-by-step explanation:

Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...

  m +m/4 +3m/2 > 22

This has solution ...

  (11/4)m > 22

   m > (4/11)22

   m > 8 . . . . . . . . the solution to the inequality

If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).

The solution set will be ...

  m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)

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