Which expressions are equivalent to -2.5(1-2n)-1.5n? Select ALLthat apply.
A:-2.5-3.5n
B:-2.5+3.5n
C:-2.5-6.5n
D:-2.5-n(5-1.5)
E:-2.5+n(5-1.5)
My answers are: B and E
Your answers is correct becouse:
- 2.5 ( 1 - 2 n ) - 1.5 n =
- 2.5 ∙ 1 - 2.5 ∙ ( - 2 n ) - 1.5 n =
- 2.5 + 5 ∙ n - 1.5 n =
- 2 .5 + 3.5 n =
3.5 n - 2.5
Answer B:
- 2.5 + 3.5 n = 3.5 n - 2.5
Answer E:
- 2.5 + n ( 5 - 1.5 ) =
- 2.5 + n ∙ 3.5 =
- 2.5 + 3.5 n =
3.5 n - 2.5
Do you think there are any more answers?
There are just two correct answers. B and E.
- 2.5 ( 1 - 2 n ) - 1.5 n =
- 2.5 ∙ 1 - 2.5 ∙ ( - 2 n ) - 1.5 n =
- 2.5 + 5 ∙ n - 1.5 n =
- 2 .5 + 3.5 n =
3.5 n - 2.5
If you analyse all offered answers:
A:
- 2.5 - 3.5 n = - 3.5 n - 2.5
not equal 3.5 n - 2.5
B:
- 2.5 + 3.5 n = 3.5 n - 2.5
equal 3.5 n - 2.5
C:
- 2.5 - 6.5 n = - 6.5 n - 2.5
not equal 3.5 n - 2.5
D:
- 2.5 - n ( 5 -1.5 ) = - 2.5 - n ∙ 3.5 = - 3.5 n - 2.5
not equal 3.5 n - 2.5
E:
- 2.5 + n ( 5 -1.5 ) = - 2.5 + n ∙ 3.5 = 3.5 n - 2.5
equal 3.5 n - 2.5
To find the equivalent expressions to -2.5(1-2n)-1.5n, we can simplify the given expression step by step.
Step 1: Distribute -2.5 to the terms inside the parentheses:
-2.5 * 1 = -2.5
-2.5 * -2n = 5n
The expression becomes: -2.5 + 5n - 1.5n
Step 2: Combine like terms:
The terms 5n and -1.5n can be combined to give 3.5n.
The expression becomes: -2.5 + 3.5n
Now, let's compare the simplified expression to each of the options given:
A: -2.5 - 3.5n - This is not equivalent to the simplified expression. Incorrect.
B: -2.5 + 3.5n - This is equivalent to the simplified expression. Correct.
C: -2.5 - 6.5n - This is not equivalent to the simplified expression. Incorrect.
D: -2.5 - n(5-1.5) - This is not the same as the simplified expression. Incorrect.
E: -2.5 + n(5-1.5) - This is equivalent to the simplified expression. Correct.
Therefore, the expressions that are equivalent to -2.5(1-2n)-1.5n are options B and E.