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After simplifying, which expressions are equivalent? Check the three that apply.

NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.
(3 points)
• -0.46 + (6b - 9.5a)
• (4.3a - 7.16) + (5.2a - 9.3b)
• (-9.36 + a) + (-7.16 + 8.5a)
• 9.5а - 16.46
• (5.2a + 6.16) + (4.3a + 4b)

1 answer

To determine which expressions are equivalent, we need to simplify each expression.

  1. Expression 1: \[ -0.46 + (6b - 9.5a) = -9.5a + 6b - 0.46 \]

  2. Expression 2: \[ (4.3a - 7.16) + (5.2a - 9.3b) = (4.3a + 5.2a) + (-7.16 - 9.3b) = 9.5a - 9.3b - 7.16 \]

  3. Expression 3: \[ (-9.36 + a) + (-7.16 + 8.5a) = a + 8.5a - 9.36 - 7.16 = 9.5a - 16.52 \]

  4. Expression 4: \[ 9.5a - 16.46 \]

  5. Expression 5: \[ (5.2a + 6.16) + (4.3a + 4b) = (5.2a + 4.3a) + (6.16 + 4b) = 9.5a + 4b + 6.16 \]

Now we compare the simplified forms:

  • Expression 1: \(-9.5a + 6b - 0.46\)
  • Expression 2: \(9.5a - 9.3b - 7.16\)
  • Expression 3: \(9.5a - 16.52\)
  • Expression 4: \(9.5a - 16.46\)
  • Expression 5: \(9.5a + 4b + 6.16\)

The expressions that have the same form and are equal can be selected as equivalent.

From our comparisons:

  1. Expression 4: \(9.5a - 16.46\) is a distinct expression.
  2. Expression 3: \(9.5a - 16.52\) is distinct from Expression 4.
  3. No other expressions seem to have the same simplified form.

It looks like there are no equivalent expressions among the simplified ones. Thus, the grouping does not satisfy 3 matches. If you want to select based on options, check your expressions accordingly.

If you find that some have clearing or additional segments that match up numerically according to parameter base with \(a\) and \(b\), consider correcting within each case dynamically as expressions appear.