Answer :
To find which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], let's simplify the original expression by combining the constant terms:
1. Original Expression:
[tex]\[
8.9x + 6.2 + 8.7
\][/tex]
Combine [tex]\(6.2 + 8.7\)[/tex]:
[tex]\[
8.9x + 14.9
\][/tex]
Now, let's check each provided expression to see if they simplify to [tex]\(8.9x + 14.9\)[/tex]:
1. [tex]\(9x + 6 + 9\)[/tex]:
- Simplify by combining the constants [tex]\(6 + 9\)[/tex], which gives:
[tex]\[
9x + 15
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- Combine constants [tex]\(8.9 + 6.2\)[/tex], which gives:
[tex]\[
15.1 + 8.7x
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- Combine constants [tex]\(8.7 + 6.2\)[/tex], which gives:
[tex]\[
8.9x + 14.9
\][/tex]
- This is equivalent to the original expression.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Combine constants [tex]\(8.7 + 6.2\)[/tex], which gives:
[tex]\[
8.9x + 14.9
\][/tex]
- This is equivalent to the original expression.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- Combine all the numbers [tex]\(6.2 + 8.7 + 8.9\)[/tex], which gives:
[tex]\[
23.8
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Combine constants [tex]\(6.2 + 8.7\)[/tex], which gives:
[tex]\[
14.9 + 8.9x
\][/tex]
- This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- This simplifies to:
[tex]\[
15.9 + 6.2x
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
Thus, the expressions that are equivalent 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]
1. Original Expression:
[tex]\[
8.9x + 6.2 + 8.7
\][/tex]
Combine [tex]\(6.2 + 8.7\)[/tex]:
[tex]\[
8.9x + 14.9
\][/tex]
Now, let's check each provided expression to see if they simplify to [tex]\(8.9x + 14.9\)[/tex]:
1. [tex]\(9x + 6 + 9\)[/tex]:
- Simplify by combining the constants [tex]\(6 + 9\)[/tex], which gives:
[tex]\[
9x + 15
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- Combine constants [tex]\(8.9 + 6.2\)[/tex], which gives:
[tex]\[
15.1 + 8.7x
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- Combine constants [tex]\(8.7 + 6.2\)[/tex], which gives:
[tex]\[
8.9x + 14.9
\][/tex]
- This is equivalent to the original expression.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Combine constants [tex]\(8.7 + 6.2\)[/tex], which gives:
[tex]\[
8.9x + 14.9
\][/tex]
- This is equivalent to the original expression.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- Combine all the numbers [tex]\(6.2 + 8.7 + 8.9\)[/tex], which gives:
[tex]\[
23.8
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Combine constants [tex]\(6.2 + 8.7\)[/tex], which gives:
[tex]\[
14.9 + 8.9x
\][/tex]
- This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- This simplifies to:
[tex]\[
15.9 + 6.2x
\][/tex]
- This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
Thus, the expressions that are equivalent 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]
