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could you please check my answer for this: -61=-5(5r-4)+4(3r-4) the answer is -65=-13r

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2 Answers

Dear Ahmad,
 
-61 = -5(5r - 4) + 4(3r - 4)
 
from which
 
-61 = -25r +20 +12r -16
 
-61 = r(12 - 25) + 4
 
-65 = -13r  (You are right, but we can carry things a step further)
 
-13r = -65
 
r = (-65/-13) = 5
Hello Ahmad -

Your work thus far is excellent! You correctly expanded the information, combined the unknowns and the constants, and came up with -65 = -13r . However this is an EQUATION (note the = sign) so you are to SOLVE for the unknown. (In this case, r.)  (In earlier lessons you were simplifying EXPRESSIONS (no equal sign, so that is likely your confusion on finishing this.
 
So, by tradition, the unknown should be on the left side. (Does not matter - answer is the same either way!)
 
So you would start at
 
-13r = -65
 
What do you do next?
 
Since it is an equation (both sides are equal) anything you do to one side you must do to the other to REMAIN equal. So to get only 1 r on the left, you could divide BOTH sides by... ________?
 
Let's try to fill in my blank with 13. You now have:
 
-13r /13 = -65 /13
 
On the left side, 13 will go into 13 one time. We aren't touching the negative at this moment. 
 
On the right side, 13 goes into 65 how many times?
 
But that leaves us with
 
-r =  - 5
 
What happens if we multiply both sides by a -1?
 
-1 * -r = -1 * -5
 
When we multiply a negative times a negative, the result is positive, correct?
 
So the negative r becomes a positive (which is required if we are solving for r, not negative r!), and since the right side is also two negatives, it also becomes positive.
 
So the final answer is _______?
 
Yes, it is
r = 5
 
 
 
But I am betting you already knew this, once I said you needed to solve for r, because you had done all the difficult work expanding the original problem. You just forgot to 'solve for the unknown' since it was an equation, not an expression. Keep up the good work!
 
         ---Russ