To simplify each expression, we need to combine like terms. This involves adding or subtracting the coefficients of the same variable and combining constant terms.
For \((2x - 4) + (x - 3)\), combine the \(x\) terms and the constant terms.
For \((2x - 4) - (-x - 3)\), distribute the negative sign and then combine like terms.
For \((2x - 4) + (-x + 3)\), combine the \(x\) terms and the constant terms.
Step 1: Simplify the First Expression
To simplify \((2x - 4) + (x - 3)\), combine the like terms:
Combine the \(x\) terms: \(2x + x = 3x\)
Combine the constant terms: \(-4 - 3 = -7\)
The simplified expression is \(3x - 7\).
Step 2: Simplify the Second Expression
To simplify \((2x - 4) - (-x - 3)\), first distribute the negative sign:
The expression becomes \((2x - 4) + x + 3\)
Now, combine the like terms:
Combine the \(x\) terms: \(2x + x = 3x\)
Combine the constant terms: \(-4 + 3 = -1\)
The simplified expression is \(3x - 1\).
Step 3: Simplify the Third Expression
To simplify \((2x - 4) + (-x + 3)\), combine the like terms: