How do I solve for a variable when it is on both sides like: 5y + 3 = 4y -1?

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We want the variable on just one side of the equal sign, so we have to get rid of one of them.  In this case 5y + 3 = 4y - 1, we want to get rid of the 5y or the 4y, your choice.  Say we choose to get...

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We want the variable on just one side of the equal sign, so we have to get rid of one of them.  In this case 5y + 3 = 4y - 1, we want to get rid of the 5y or the 4y, your choice.  Say we choose to get rid of the 4y.  Since it is a positive 4y we would have to subtract 4y.  5y + 3 = 4y - 4y -1.  But let's not forget, if we do it to one side of the equal sign, we must do it to the other, so; 5y - 4y + 3 = 4y - 4y - 1.  This gives us y + 3 = -1, eliminating the variable from one of the sides of the equal sign.

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You can add, subtract, multiply, divide, or perform any other mathematical opperation to both sides of the equation. So this includes adding or subtracting by the variable itself.

So to solve your problem, move the 4y onto the other side by subtracting it from both sides, like this:

5y + 3 = 4y - 1

5y - 4y + 3 = 4y - 1 - 4y

y + 3 = -1

y = -4

Plug it in and check:

5(-4) + 3 = 4(-4) - 1

-20 + 3 = -16 - 1

-17 = -17 check.

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