Question

Select all of the expressions equivalent to (834+312m)−(814+214m).
834+312m+(−814)+214m
834+312m+(−814)+(−214m)
[834+(−814)]+[312m+(−214m)]
[834+(−814)]+(312m+214m)
12
+ 534
m
12
+114
m

Answer 1

To simplify the expression \((834 + 312m) - (814 + 214m)\), we can follow these steps:

1. Rewrite the expression by distributing the negative sign:
\[
834 + 312m - 814 - 214m
\]

2. Combine like terms:
- For the constant terms: \(834 - 814 = 20\)
- For the \(m\) terms: \(312m - 214m = 98m\)

So the simplified expression is:
\[
20 + 98m
\]

Next, we will assess which of the provided expressions are equivalent to \(20 + 98m\):

1. **Expression:** \(834 + 312m + (-814) + 214m\)
**Simplifies to:** \(834 - 814 + 312m + 214m = 20 + 98m\)
**Result:** Equivalent

2. **Expression:** \(834 + 312m + (-814) + (-214m)\)
**Simplifies to:** \(834 - 814 + 312m - 214m = 20 + 98m\)
**Result:** Equivalent

3. **Expression:** \([834 + (-814)] + [312m + (-214m)]\)
**Simplifies to:** \(20 + 98m\)
**Result:** Equivalent

4. **Expression:** \([834 + (-814)] + (312m + 214m)\)
**Simplifies to:** \(20 + 526m\)
**Result:** Not equivalent

5. **Expression:** \(12 + 534m\)
**Result:** Not equivalent (since we have \(20 + 98m\))

6. **Expression:** \(12 + 114m\)
**Result:** Not equivalent (since we have \(20 + 98m\))

In summary, the equivalent expressions are:
- \(834 + 312m + (-814) + 214m\)
- \(834 + 312m + (-814) + (-214m)\)
- \([834 + (-814)] + [312m + (-214m)]\)