Answered

Use algebra tiles to determine which expression is equivalent to $-5 x+4$.


A$(-3 x)+3+(-2 x)+1$
B$(-3 x)+3+(2 x)+1$
C$(-3 x)+(-3)+(-2 x)+(-1)$
D$3 x+3+2 x+1$

Verified Answer :

  • Simplify the target expression \(-5x + 4\).
  • Evaluate each option by combining like terms:
  1. \((-3x) + 3 + (-2x) + 1 = -5x + 4\)
  2. \((-3x) + 3 + (2x) + 1 = -x + 4\)
  3. \((-3x) + (-3) + (-2x) + (-1) = -5x - 4\)
  4. \(3x + 3 + 2x + 1 = 5x + 4\)
  • The only expression equivalent to \(-5x + 4\) is the first one.
  • Final Answer: \(\boxed{1}\)

Explanation

  1. Problem Analysis

We are given the expression \(-5x + 4\) and need to identify which of the four provided options simplifies to this expression by combining like terms. The expressions are:

  1. \((-3x) + 3 + (-2x) + 1\)
  2. \((-3x) + 3 + (2x) + 1\)
  3. \((-3x) + (-3) + (-2x) + (-1)\)
  4. \(3x + 3 + 2x + 1\)

We will group the terms involving \(x\) together and the constant terms together for each expression to check for equality with \(-5x + 4\).

  1. Evaluating the Options

We simplify each option by grouping like terms:

  • Option 1: \((-3x) + (-2x) + 3 + 1 = (-3-2)x + (3+1) = -5x + 4\). This matches our target expression.
  • Option 2: \((-3x) + (2x) + 3 + 1 = (-3+2)x + (3+1) = -x + 4\). This does not match.
  • Option 3: \((-3x) + (-2x) + (-3) + (-1) = (-3-2)x + (-3-1) = -5x - 4\). This does not match.
  • Option 4: \(3x + 2x + 3 + 1 = (3+2)x + (3+1) = 5x + 4\). This does not match.

Comparing these results to our target \(-5x + 4\), only Option 1 is equivalent.

  1. Conclusion

After simplifying each expression by grouping the variable terms (\(x\)) and the constant terms, we found that only the first expression, \((-3x) + 3 + (-2x) + 1\), simplifies to \(-5x + 4\). Thus, the correct choice is Option 1. The final answer is \(\boxed{1}\).

Examples

Algebra tiles provide a visual way to model algebraic expressions. Imagine you are working in a warehouse where you have special bins for 'x' items and regular bins for unit items. If you have a bin with \(-3x\) tiles and another with \(-2x\) tiles, putting them together results in a bin with \(-5x\) tiles. Combining a bin of 3 units and a bin of 1 unit results in a bin of 4 units. This method helps in organizing and simplifying complex inventories or budgets efficiently.

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