Questions: Combine like terms (simplify). (2x-4)+(x-3) (2x-4)-(-x-3) (2x-4)+(-x+3) (2x-4)-(x+3)

Combine like terms (simplify).
(2x-4)+(x-3)
(2x-4)-(-x-3)
(2x-4)+(-x+3)
(2x-4)-(x+3)
Transcript text: Combine like terms (simplify). \[ \begin{array}{l} (2 x-4)+(x-3) \\ (2 x-4)-(-x-3) \\ (2 x-4)+(-x+3) \\ (2 x-4)-(x+3) \end{array} \]
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Solution

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Solution Steps

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.

  1. For \((2x - 4) + (x - 3)\), combine the \(x\) terms and the constant terms.
  2. For \((2x - 4) - (-x - 3)\), distribute the negative sign and then combine like terms.
  3. 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:

  • Combine the \(x\) terms: \(2x - x = 1x\)
  • Combine the constant terms: \(-4 + 3 = -1\)

The simplified expression is \(x - 1\).

Final Answer

\(\boxed{x - 1}\)

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