Question

HELP ASAP!!!!!!

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
3.)-5 < 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

Answer 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.