he solution set is
{
x
∣
x
>
1
}
.
Explanation
For each of these inequalities, there will be a set of
x
-values that make them true. For example, it's pretty clear that large values of
x
(like 1,000) work for both, and negative values (like -1,000) will not work for either.
Since we're asked to solve a "this OR that" pair of inequalities, what we'd like to know are all the
x
-values that will work for at least one of them. To do this, we solve both inequalities for
x
, and then overlap the two solution set
The best way to find it is to reduce each ratio you work with to its
lowest terms,and see which ones are equal. To reduce a ratio to its
lowest terms, divide each number by their greatest common factor.
First, the one that you're trying to match: <u>49:35</u> .
The greatest common factor of 49 and 35 is 7 .
Divide each number by 7 . . . <em>7:5</em> . . . <u>that's</u> what you have to match.
<u>7:4</u>
Their greatest common factor is ' 1 '.
No help at all, and this one is not it.
<u>14:25</u>
Again, their greatest common factor is '1 '.
No help at all, and this one is not it.
<u>21:15</u>
Their greatest common factor is ' 3 '.
Divide both numbers by 3 . . . <em>7:5 </em>.
That's it !
7/8 x = 21
7x = 21×8
7x = 168
x = 24
