1. ashlynn143

PROBLEM $-\frac{ 2 }{ 3 }t + 2 -\frac{ 4 }{ 3 } t \le- 4$

2. sandra

So first thing to do is combine like terms - in this case the two fractions that are both in terms of "t".

3. ashlynn143

choices $a : t \ge 1$ $b : t \le 3$ $c : t \ge 3$ $d : t \le 1$

4. sandra

-2t/3 -4t/3 +2 <= -4 -6t/3 + 2 <=4

5. sandra

Now notice that (-6/3)t can be reduced. It's just -2t. So -2t + 2 <= -4 -2t <= -4 - 2 -2t <= -6

6. sandra

Do you know the last step?

7. ashlynn143

kinda hold on i will see if i get a correct answer

8. ashlynn143

ok so |dw:1357807306782:dw|

9. ashlynn143

my answer is $t \ge -3$

10. sandra

Ok close - you remembered to change the direction of the <=. But! -6/-2 = 3. So t >= 3.

11. ashlynn143

oh i thought that it was negative thanks you are a great explainer

12. sandra

When you divide both sides of an inequality by a negative number, you do change the direction of the inequality.

13. sandra

No problem, good work and good luck!

14. ashlynn143

thanks