Answer :
To find which expressions are equivalent to the expression [tex]\(8.9x + 6.2 + 8.7\)[/tex], we'll first simplify the original expression and then check each given option.
1. Simplify the original expression:
The expression [tex]\(8.9x + 6.2 + 8.7\)[/tex] can be simplified by combining the constants:
[tex]\[
8.9x + (6.2 + 8.7) = 8.9x + 14.9
\][/tex]
So the expression simplifies to [tex]\(8.9x + 14.9\)[/tex].
2. Check each option:
a) [tex]\(9x + 6 + 9\)[/tex]:
Simplify this:
[tex]\[
9x + (6 + 9) = 9x + 15
\][/tex]
This is not the same as [tex]\(8.9x + 14.9\)[/tex].
b) [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
Rearrange for comparison:
[tex]\[
8.7x + (8.9 + 6.2) = 8.7x + 15.1
\][/tex]
This is not the same as [tex]\(8.9x + 14.9\)[/tex].
c) [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
Combine constants:
[tex]\[
8.9x + (8.7 + 6.2) = 8.9x + 14.9
\][/tex]
This matches the simplified form of the original expression.
d) [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
Combine constants:
[tex]\[
8.9x + (8.7 + 6.2) = 8.9x + 14.9
\][/tex]
This also matches the simplified form of the original expression.
e) [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
Simplify this:
[tex]\[
6.2 + 8.7 + 8.9 = 23.8
\][/tex]
This is not an expression in terms of [tex]\(x\)[/tex] and doesn't match.
f) [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
Rearrange for comparison:
[tex]\[
8.9x + (6.2 + 8.7) = 8.9x + 14.9
\][/tex]
This matches the simplified form of the original expression.
g) [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
Rearrange and simplify:
[tex]\[
6.2x + (8.9 + 8.7) = 6.2x + 17.6
\][/tex]
This is not the same as [tex]\(8.9x + 14.9\)[/tex].
3. Conclusion:
The expressions which are equivalent to the original expression [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. Simplify the original expression:
The expression [tex]\(8.9x + 6.2 + 8.7\)[/tex] can be simplified by combining the constants:
[tex]\[
8.9x + (6.2 + 8.7) = 8.9x + 14.9
\][/tex]
So the expression simplifies to [tex]\(8.9x + 14.9\)[/tex].
2. Check each option:
a) [tex]\(9x + 6 + 9\)[/tex]:
Simplify this:
[tex]\[
9x + (6 + 9) = 9x + 15
\][/tex]
This is not the same as [tex]\(8.9x + 14.9\)[/tex].
b) [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
Rearrange for comparison:
[tex]\[
8.7x + (8.9 + 6.2) = 8.7x + 15.1
\][/tex]
This is not the same as [tex]\(8.9x + 14.9\)[/tex].
c) [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
Combine constants:
[tex]\[
8.9x + (8.7 + 6.2) = 8.9x + 14.9
\][/tex]
This matches the simplified form of the original expression.
d) [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
Combine constants:
[tex]\[
8.9x + (8.7 + 6.2) = 8.9x + 14.9
\][/tex]
This also matches the simplified form of the original expression.
e) [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
Simplify this:
[tex]\[
6.2 + 8.7 + 8.9 = 23.8
\][/tex]
This is not an expression in terms of [tex]\(x\)[/tex] and doesn't match.
f) [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
Rearrange for comparison:
[tex]\[
8.9x + (6.2 + 8.7) = 8.9x + 14.9
\][/tex]
This matches the simplified form of the original expression.
g) [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
Rearrange and simplify:
[tex]\[
6.2x + (8.9 + 8.7) = 6.2x + 17.6
\][/tex]
This is not the same as [tex]\(8.9x + 14.9\)[/tex].
3. Conclusion:
The expressions which are equivalent to the original expression [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]
