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Question

Select all expressions that are equivalent to this algebraic expression.

(2x−1)−3.25(x+3)


(4 points)
Responses

2x−1−3.25x−9.75
2 x minus 1 minus 3 point 2 5 x minus 9 point 7 5

2x−3.25x−1−9.75
2 x minus 3 point 2 5 x minus 1 minus 9 point 7 5

−1.25x−1−9.75
negative 1 point 2 5 x minus 1 minus 9 point 7 5

−1.25x−10.75
negative 1 point 2 5 x minus 10 point 7 5

2x−1−3.25x+9.75
2 x minus 1 minus 3 point 2 5 x plus 9 point 7 5

1.25x+10.75
1 point 2 5 x plus 10 point 7 5

−1.25x−4
negative 1 point 2 5 x minus 4

Answer 1

To determine which expressions are equivalent to the given algebraic expression \((2x−1)−3.25(x+3)\), let's simplify it step by step.

1. Distribute \(-3.25\) into \((x + 3)\): \[ -3.25(x + 3) = -3.25x - 9.75 \]

2. Rewrite the original expression: \[ (2x - 1) - (3.25x + 9.75) = 2x - 1 - 3.25x - 9.75 \]

3. Combine like terms: \[ (2x - 3.25x) + (-1 - 9.75) = -1.25x - 10.75 \]

Now, let's compare the simplified expression \(-1.25x - 10.75\) with the given responses to see which ones match.

1. \(2x−1−3.25x−9.75\):

   • Simplifies to \(-1.25x - 10.75\) (Equivalent)

2. \(2x−3.25x−1−9.75\):

   • Simplifies to \(-1.25x - 10.75\) (Equivalent)

3. \(−1.25x−1−9.75\):

   • Simplifies to \(-1.25x - 10.75\) (Equivalent)

4. \(−1.25x−10.75\):

   • This is already simplified to \(-1.25x - 10.75\) (Equivalent)

5. \(2x−1−3.25x+9.75\):

   • This simplifies to \(-1.25x + 8.75\) (Not Equivalent)

6. \(1.25x+10.75\):

   • This is not equivalent as it’s a positive coefficient (Not Equivalent)

7. \(−1.25x−4\):

   • Simplifies to \(-1.25x - 4\) (Not Equivalent)

The equivalent expressions to \((2x−1)−3.25(x+3)\) are:

• \(2x−1−3.25x−9.75\)
• \(2x−3.25x−1−9.75\)
• \(−1.25x−1−9.75\)
• \(−1.25x−10.75\)

Thus, the correct responses are:

• 2x−1−3.25x−9.75
• 2x−3.25x−1−9.75
• −1.25x−1−9.75
• −1.25x−10.75