Simple distribution question regarding negatives

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yeewooo

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Jun 28, 2021
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-5 (2y - 15)

Because the 15 is being multiplied by -5, will that turn the subtraction symbol into a +?
so,

-10y + 75

or am I overthinking it, and -10y -75 is still correct?
 
Just to add more context, the question is a basic substitution equation:

-5x + 4y = 3
x = 2y -15

My attempt at it gave me: x = 11 and y = 13. I think I may have dun goofed at that distribution part with a negative but I dont know. Help pls!
 
yeewooo said:
-5 (2y - 15)

Because the 15 is being multiplied by -5, will that turn the subtraction symbol into a +?
so,

-10y + 75

or am I overthinking it, and -10y -75 is still correct?
Click to expand...
-5 (2y - 15) = -10*y + 75
 
yeewooo said:
Just to add more context, the question is a basic substitution equation:

-5x + 4y = 3
x = 2y -15

My attempt at it gave me: x = 11 and y = 13. I think I may have dun goofed at that distribution part with a negative but I dont know. Help pls!
Click to expand...
Please share your "numerical" steps to get to the answer.
 
***Correction: my y from above is wrong, and I forgot to change it prior to typing this. I got y = -41 instead, not 11
Hi, here's my steps:

-5x + 4y = 3
x = 2y - 15

-5(2y - 15) + 4y = 3

-10y - 75 + 4y = 3

+75 -6y - 75 = 3 +75

-6y / -6 = 78 / -6

y = -13


x = 2(-13) -15

x = -26 -15

x = -41


-5 (-41) + 4(-13) = 3
205 + (-52) = 3 <------ this is my mistake where it doesn't balance, so I tried tracking it back, and thought maybe the distribution with a negative was my mistake

Also, since my question was initially just an arithmetic problem (I think?) forgive me if this topic is in the wrong thread
 
By the distributive law of multiplication a(by + c) = (ab)y + (ac). You do have to keep track of the signs.

In your case, a = -5, b = 2, c = -15. Thus -5(2y + -15) = (-5 * 2)y + (-5 * -15) = -10y + 75.

-Dan
 
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