Colin G.

asked • 10/07/16

(-9/7a) + (2/3a)=-65/21

please help solve the equation



thanks much in advance

Michael A.

tutor
Colin, is the a in the numerator or the denominator for the terms listed above?
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10/07/16

Colin G.

neither it's centered near the fraction. the same on the other side as well
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10/07/16

Michael A.

tutor
Then I assume that it means to multiply both fractions by a, which suggests that the a is in the numerator. 
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10/07/16

Michael A.

tutor
Thanks for the clarification, Colin.
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10/07/16

1 Expert Answer

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Michael A. answered • 10/07/16

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Assuming that we have:
 
(-9/7)a + (2/3)a = -65/21
 
Let's first multiply both sides of the equation by 21 to clear any fractions. 
 
-27a + 14a = -65
 
Combine like terms to get:
 
-13a = -65
 
Divide both sides by -13 to solve for a.
 
a = 5
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Colin G.

thanks much
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10/07/16

Michael A.

tutor
Welcome!
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10/07/16

Colin G.

could you kindly help me with this problem please 
 
Please help Solve the compound inequality, the solution has to be in interval notation, and if you can graph the solution set on a number line. thanks much

- 14/5 < - 7/6k < 7/15

the - sign is centered in the fractions
the k is centered after the fraction
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10/07/16

Michael A.

tutor
Yes, Colin. Although next time you may want to post your question to the forum in order to get a more immediate response. When you add a question to the Comment section, it doesn't appear on the board. Thanks!
 
To solve the compound inequality, break it into parts. We first examine the first inequality:
 
-14/5 < -7/6 k
 
Let's first multiply thru by 30 to eliminate the fractions.
 
-84 < -35 k
 
Now, we must divide both sides by -35, remembering to flip the inequality symbol, so that we may solve for k.
 
84/35 > k
 
This can be reduced by dividing top and bottom by 7 such that we wind up with:
 
k < 12/5
 
Now, let's examine the second inequality:
 
-7/6 k < 7/15
 
Again, we can multiply both sides by 30 to clear the fractions.
 
-35 k < 14
 
Dividing both sides by -35 and flipping the inequality symbol, we get:
 
k > -14/35
 
Now, we divide top and bottom by 7 to reduce this to:
 
k > -2/5
 
The entire solution is:
 
-2/5 < k < 12/5, which can be written as
 
(-2/5, 12/5)
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10/07/16

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