Question

solve each compound inequality for x

7b - 4 < b + 2 < 9 + 2b

Answer 1

Is it one all together?

Answer 2

yes I think the b+2 in the middle makes it a (and)

Answer 3

7b - 4 < b + 2 and b + 2 < 9 + 2b

Answer 4

7b - 4 < b + 2 < 9 + 2b

subtract 7b from the left

-4 <b-7b + 2 <9 + 2b

subtract 2b from the right

-4 < -6b + 2 -2b <9

simplify

-4 < -8b + 2 < 9

subtract 2 from the inside which means you have to subtract 2 from both sides

-4 -2 < -8b < 9-2

simplify

-6 < -8b < 7

divide both sides by -8. when you divide over inequalities with a negative you reverse the inequality

-6/-8 > b >-7/8

simplify

3/4 > b > -7/8

rewrite like the original form

-7/8 < b < 3/4

Answer 5

7b - 4 < b + 2 and b + 2 < 9 + 2b

solve the left side

7b - b < 2 + 4

6b < 6

b < 1

solve the right side

2-9 < 2b-b

-7 <b

so

-7 < b < 1

not sure why my first method didn't work but this is now the correct answer as confirmed by wolfram

http://www.wolframalpha.com/input/?i=7b+-+4+%3C+b+%2B+2+%3C+9+%2B+2b

Answer 6

thanksssss!!!!!!!!