-|8X-3Y|+|2Y+5X|.....SOLVE
what's to solve? there's just an expression
if 8x+3y>=0 and 2y+5x>=0, then the expression is
-(8x+3y)+(2y+5x) = -3x-y
if 8x+3y<0 and 2y+5x>=0, then the expression is
(8x+3y)+(2y+5x) = 13x+5y
if 8x+3y>=0 and 2y+5x<0, then the expression is
-(8x+3y)-(2y+5x) = -13x-5y
if 8x+3y<0 and 2y+5x<0, then the expression is
(8x+3y)-(2y+5x) = 3x+y
To solve the expression -|8X - 3Y| + |2Y + 5X|, you need to simplify each absolute value separately and then combine the resulting expressions.
1. Simplify the expression inside the first absolute value:
|-|8X - 3Y||
The inner expression, 8X - 3Y, can be either positive or negative. To find the positive form, remove the absolute value signs:
8X - 3Y, when 8X - 3Y ≥ 0
To find the negative form, change the sign of the inner expression:
-(8X - 3Y), when 8X - 3Y < 0
Therefore, we have two cases:
Case 1: 8X - 3Y ≥ 0
|-|8X - 3Y|| = 8X - 3Y
Case 2: 8X - 3Y < 0
|-|8X - 3Y|| = -(8X - 3Y) = -8X + 3Y
2. Simplify the expression inside the second absolute value:
|2Y + 5X|
There are no assumptions needed here since we don't have any inequality or negative form. So we simply remove the absolute value signs:
|2Y + 5X| = 2Y + 5X
3. Combine the simplified expressions from steps 1 and 2:
-|8X - 3Y| + |2Y + 5X| = -(8X - 3Y) + (2Y + 5X)
Now, you can simplify the expression further by distributing the negatives and combining like terms:
-(8X - 3Y) + (2Y + 5X) = -8X + 3Y + 2Y + 5X
Simplify by combining like terms:
-8X + 5X + 3Y + 2Y = -3X + 5Y
Therefore, the simplified form of the expression -|8X - 3Y| + |2Y + 5X| is -3X + 5Y.