Question

Given: x - 6 1/3≤ 1 1/2

Choose the solution set.
a. {x | x ∈ R, x ≤ 7 5/6}
b. {x | x ∈ R, x ≤ 7 2/5}
c. {x | x ∈ R, x ≤ 5 1/6}

Answer 1

Can you be a bit clearer in how the inequality is actually written? Do you mean:
\[(x - 6)(\frac{ 1 }{ 3}) \le (1)(\frac{ 1 }{ 2 })\]

Answer 2

yes, sorry i dont know how to type it that way

Answer 3

That's no problem, thanks for clarifying. So, essentially we're looking to rearrange the inequality to find x on its own, from which we can identify the solution set. For starters, we can multiply out the brackets on each side of the inequality sign:

\[\frac{ 1 }{ 3}x -\frac{ 1 }{ 3 }(6) \le \frac{ 1 }{ 2 }\]
\[\frac{ 1 }{ 3 }x - 2 \le 2\]

I'll leave it to you to finish this one off. Remember that we can treat the inequality sign as an '=' sign effectively when we're adding, subtracting or multiplying positive values across both sides in order to get x on its own (i.e. we ignore it). If we multiply across by a negative number, then we must 'flip' the sign of the inequality when doing so (i.e. it would change from <= to >= here), but we don't have to worry about this at all for this question.

The first thing to do is to get rid of the '-2' on the left-hand side. Once you have done that , you can get rid of the fraction which x is multiplied to on this side by multiplying across the whole inequality appropriately. This should leave you with x on its own, hopefully. Good luck!

Answer 4

Sorry once more, I've made another mistake, this time in the inequality I have worked out above in my answer. Once you multiply out the brackets, the right-hand side should clearly by 1/2 and not 2 as I show above. So, the overall equation should be:

\[\frac{ 1 }{ 3 }x - 2 \le \frac{ 1 }{ 2 }\]

Apologies for the error! :)

Answer 5

thank you for walking me through that, and that is no problem (: