Solve and graph the inequalities below. describe your graphs using words as illustrated in the sample below. sample: part 1: the solution is x > 5 and x< =9. part 2: there would be an open circle on 5 and a closed circle on 9. part 3: the shading is between the two numbers.  be sure that you have included all three parts when answering each question. "greater than or equal to" would be typed > =. "less than or equal to" would be typed < =. 1.) d - 1 > -3 and d + 2 < 5 2.) -3k + 7 > -5 and -7k + 5 < -2 < 2y - 3 < 23 (hint: refer to example 2 in the lesson.) 4.)x - 4 < 5 or x + 2 > 15 5.) 5x - 4 > 6 or -4x + 5 > 1

1.) d - 1 > -3 and d + 2 < 5
d-1>-3→d-1+1>-3+1→d>-2
d+2<5→d+2-2<5-2→d<3
Part 1: The solution is d>-2 and d<3. 
Part 2: There would be an open circle on -2 and an open circle on 3.
Part 3: The shading is between the two numbers.

2.) -3k + 7 > -5 and -7k + 5 < -2
-3k+7>-5→-3k+7-7>-5-7→-3k>-12→(-1/3)(-3k>-12)→k<4
-7k+5<-2→-7k+5-5<-2-5→-7k<-7→(-1/7)(-7k<-7)→k>1
Part 1: The solution is k>1 and k<4. 
Part 2: There would be an open circle on 1 and an open circle on 4.
Part 3: The shading is between the two numbers.
 
3.)-5 < 2y - 3 < 23 (Hint: refer to example 2 in the lesson)
-5<2y-3<23→-5+3<2y-3+3<23+3→-2<2y<26→-2/2<2y/2<26/2→-1<y<13
Part 1: The solution is y>-1 and y<13. 
Part 2: There would be an open circle on -1 and an open circle on 13.
Part 3: The shading is between the two numbers.

4.)x - 4 < 5 or x + 2 > 15
x-4<5→x-4+4<5+4→x<9
x+2>15→x+2-2>15-2→x>13
Part 1: The solution is x>9 or x>13. 
Part 2: There would be an open circle on 9 and an open circle on 13.
Part 3: The shading is from 9 to the left and from 13 to the right.

5.) 5x - 4 > 6 or -4x + 5 > 1
5x-4>6→5x-4+4>6+4→5x>10→5x/5>10/5→x>2
-4x+5>1→-4x+5-5>1-5→-4x>-4→(-1/4)(-4x>-4)→x<1
Part 1: The solution is x<1 or x>2. 
Part 2: There would be an open circle on 1 and an open circle on 2.
Part 3: The shading is from 1 to the left and from 2 to the right.

and y≤ -x +4 .

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

y≤ -x +4 .