ashlynn143
please help MEDALS WILL BE GIVEN



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ashlynn143
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PROBLEM
\[\frac{ 2 }{ 3 }t + 2 \frac{ 4 }{ 3 } t \le 4\]

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

ashlynn143
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choices
\[a : t \ge 1\]
\[b : t \le 3\]
\[c : t \ge 3\]
\[d : t \le 1\]

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

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

sandra
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Do you know the last step?

ashlynn143
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kinda hold on i will see if i get a correct answer

ashlynn143
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ok so dw:1357807306782:dw

ashlynn143
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my answer is
\[t \ge 3\]

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

ashlynn143
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oh i thought that it was negative thanks you are a great explainer

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

sandra
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No problem, good work and good luck!

ashlynn143
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thanks