Question

Help me please
d - 1 > -3 and d + 2 < 5

-3k + 7 > -5 and -7k + 5 < -2

-5 < 2y - 3 < 23 (Hint: refer to example 2 in the lesson.)

x - 4 < 5 or x + 2 > 15

5x - 4 > 6 or -4x + 5 > 1

Answer 1

I'll do the first one to get you started

Answer 2

d - 1 > -3

d - 1+1 > -3 +1 ... Add 1 to both sides.

d + 0 > -2

d > -2

Answer 3

d + 2 < 5

d + 2 -2 < 5 -2 ... Subtract 2 from both sides.

d + 0 < 3

d < 3

Answer 4

so the two inequalities

d - 1 > -3 and d + 2 < 5

turn into

d > -2 and d < 3

and you can flip the first inequality to get

-2 < d and d < 3

then combine the two to get the final answer

-2 < d < 3

Answer 5

Putting all that into words:
By solving for d in both inequalities we are able to tell that d must be greater than -2 and less than 3.