slayer8001 one year ago Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5. Show your work.

1. slayer8001

@peachpi

2. slayer8001

plz I really need help

3. anonymous

break this up. Do this one first $2x-3 < x + 2$

4. slayer8001

is it -1x<2x ?

5. slayer8001

@peachpi

6. anonymous

|dw:1441890766597:dw|

7. anonymous

then do $$x+2 \le 3x+5$$

8. anonymous

start by subtracting 3x from both sides

9. slayer8001

it would be the same wouldn't it?

10. anonymous

usually not.

11. slayer8001

is it -2+2<5?

12. slayer8001

after subtracting 3

13. anonymous

where did your x go? You should have -2x + 2 < 5 Then subtract the 2 from both sides

14. slayer8001

oops yeah forgot to put the x

15. slayer8001

-2x<3?

16. anonymous

right then divide by -2 and flip the sign since it's negative

17. slayer8001

-1x>0.67?

18. anonymous

x > -0.67 b/c you only flip once you divide by the negative

19. anonymous

also, you should leave it as $$x>-\frac{2}{3}$$ because it's more exact

20. slayer8001

ok

21. anonymous

If you were to graph the two solutions it would look like this|dw:1441891511708:dw|

22. anonymous

23. anonymous

So the solution is all numbers between -2/3 and 5, including 5 and you'd write it as $-\frac{ 2 }{ 3 }<x\le5$

24. slayer8001

ok thanks so much I really appreciate your help

25. anonymous

you're welcome