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Math  /  Algebra

Question{3x−[y+3x−(2y+x)]−2}−7=\{3 x-[y+3 x-(2 y+x)]-2\}-7=

Studdy Solution

STEP 1

1. We are asked to simplify the given expression.
2. The expression involves variables and constants, and we need to simplify it by combining like terms and simplifying the arithmetic.

STEP 2

1. Simplify the expression inside the innermost parentheses.
2. Simplify the expression inside the outer parentheses.
3. Simplify the entire expression by combining like terms and constants.

STEP 3

Simplify the expression inside the innermost parentheses (2y+x)(2y + x):
The expression [y+3x−(2y+x)][y + 3x - (2y + x)] can be rewritten by distributing the negative sign:
y+3x−2y−x y + 3x - 2y - x

STEP 4

Combine like terms inside the brackets:
(y−2y)+(3x−x)=−y+2x (y - 2y) + (3x - x) = -y + 2x
Now the expression becomes:
3x−(−y+2x)−2 3x - (-y + 2x) - 2

STEP 5

Distribute the negative sign and simplify the expression:
3x+y−2x−2 3x + y - 2x - 2
Combine like terms:
(3x−2x)+y−2=x+y−2 (3x - 2x) + y - 2 = x + y - 2
Subtract 7 from the expression:
x+y−2−7=x+y−9 x + y - 2 - 7 = x + y - 9
The simplified expression is:
x+y−9 \boxed{x + y - 9}

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