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Question

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
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Answer 1

To determine which expressions are equivalent to the algebraic expression \((2x - 1) - 3.25(x + 3)\), we need to simplify the expression step by step.

1. Start by distributing \(-3.25\) across \((x + 3)\): \[ -3.25(x + 3) = -3.25x - 9.75 \]

2. Substitute this back into the expression: \[ (2x - 1) - 3.25(x + 3) = (2x - 1) - (3.25x + 9.75) \]

3. Now, simplify by combining like terms: \[ 2x - 1 - 3.25x - 9.75 \] Combine the \(x\) terms: \[ 2x - 3.25x = -1.25x \] Combine the constants: \[ -1 - 9.75 = -10.75 \]

4. This gives us the simplified expression: \[ -1.25x - 10.75 \]

Now we can evaluate which of the provided options match \(-1.25x - 10.75\).

Here's the analysis for each option:

1. \(2x - 1 - 3.25x - 9.75\): This simplifies to \(-1.25x - 10.75\) (Equivalent).
2. \(2x - 3.25x - 1 - 9.75\): This simplifies to \(-1.25x - 10.75\) (Equivalent).
3. \(-1.25x - 1 - 9.75\): This simplifies to \(-1.25x - 10.75\) (Equivalent).
4. \(-1.25x - 10.75\): This is exactly the same (Equivalent).
5. \(2x - 1 - 3.25x + 9.75\): This does not simplify to \(-1.25x - 10.75\) (Not Equivalent).
6. \(1.25x + 10.75\): This is the opposite sign and hence not equivalent (Not Equivalent).
7. \(-1.25x - 4\): This does not simplify to \(-1.25x - 10.75\) (Not Equivalent).

Final Equivalent Expressions:

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

These four options are equivalent to the original expression.