Select all of the expressions equivalent to (834+312m)−(814+214m).

Question

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:

• \(834 + 312m + (-814) + 214m\)
• \(834 + 312m + (-814) + (-214m)\)
• \([834 + (-814)] + [312m + (-214m)]\)