High School

Which expressions are equivalent to [tex]8.9x + 6.2 + 8.7[/tex]? Check all that apply.

A. [tex]9x + 6 + 9[/tex]
B. [tex]8.9 + 6.2 + 8.7x[/tex]
C. [tex]8.9x + 8.7 + 6.2[/tex]
D. [tex]8.7 + 8.9x + 6.2[/tex]
E. [tex]6.2 + 8.7 + 8.9[/tex]
F. [tex]6.2 + 8.7 + 8.9x[/tex]
G. [tex]8.9 + 6.2x + 8.7[/tex]

Answer :

To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to simplify each option and compare it to the original expression.

Here's how you can evaluate each expression:

1. Original Expression: [tex]\(8.9x + 6.2 + 8.7\)[/tex]

Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].

So, the original expression simplifies to [tex]\(8.9x + 14.9\)[/tex].

Now, let's check each of the given options:

1. Option 1: [tex]\(9x + 6 + 9\)[/tex]

Simplify the constants: [tex]\(6 + 9 = 15\)[/tex].

So, this becomes [tex]\(9x + 15\)[/tex].

Compare: [tex]\(9x + 15\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].

2. Option 2: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]

Simplify the constants: [tex]\(8.9 + 6.2 = 15.1\)[/tex].

So, this becomes [tex]\(15.1 + 8.7x\)[/tex].

Compare: [tex]\(15.1 + 8.7x\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].

3. Option 3: [tex]\(8.9x + 8.7 + 6.2\)[/tex]

Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex].

So, this matches [tex]\(8.9x + 14.9\)[/tex].

Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].

4. Option 4: [tex]\(8.7 + 8.9x + 6.2\)[/tex]

Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex].

So, this becomes [tex]\(8.9x + 14.9\)[/tex].

Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].

5. Option 5: [tex]\(6.2 + 8.7 + 8.9\)[/tex]

Simplify the entire sum: [tex]\(6.2 + 8.7 + 8.9 = 23.8\)[/tex].

This expression is just a constant: [tex]\(23.8\)[/tex].

Compare: [tex]\(23.8\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].

6. Option 6: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]

Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].

So, this becomes [tex]\(14.9 + 8.9x\)[/tex].

Rearrange to match: [tex]\(8.9x + 14.9\)[/tex].

Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].

7. Option 7: [tex]\(8.9 + 6.2x + 8.7\)[/tex]

Simplify the constants: [tex]\(8.9 + 8.7 = 17.6\)[/tex].

So, this becomes [tex]\(17.6 + 6.2x\)[/tex].

Compare: [tex]\(17.6 + 6.2x\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].

The equivalent expressions to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:

- [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- [tex]\(6.2 + 8.7 + 8.9x\)[/tex]