Let () = 2 - 7 and () = -6 - 3. Find () + () and state its domain.
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<span><u><em>Answer:</em></u>
Each will have passed 17 tests and it will take 3 weeks.
<u><em>Explanation: </em></u>
Let x be the number of weeks.
The number of tests <u>Travis</u> passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.
The number of tests <u>Jenifer</u> has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.
<u>Setting these equal, we have: </u>
11+2x=2+5x.
<u>Subtract 2x from each side: </u>
11+2x-2x=2+5x-2x;
11=2+3x.
<u>Subtract 2 from each side: </u>
11-2=2+3x-2;
9=3x.
<u>Divide both sides by 3:</u>
</span>
<span>;
3=x.
It will take <u>3 weeks</u>.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.</span>
Each will have passed 17 tests and it will take 3 weeks.
<u><em>Explanation: </em></u>
Let x be the number of weeks.
The number of tests <u>Travis</u> passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.
The number of tests <u>Jenifer</u> has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.
<u>Setting these equal, we have: </u>
11+2x=2+5x.
<u>Subtract 2x from each side: </u>
11+2x-2x=2+5x-2x;
11=2+3x.
<u>Subtract 2 from each side: </u>
11-2=2+3x-2;
9=3x.
<u>Divide both sides by 3:</u>
</span>
3=x.
It will take <u>3 weeks</u>.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.</span>