Answer :
To determine which expressions are equivalent to the given expression [tex]\(8.9x + 6.2 + 8.7\)[/tex], let's break down what “equivalent” means. Two expressions are equivalent if, when simplified or rearranged, they yield the same result.
Here is the original expression:
[tex]\[ 8.9x + 6.2 + 8.7 \][/tex]
First, we can simplify this expression by combining like terms. Notice that [tex]\(6.2\)[/tex] and [tex]\(8.7\)[/tex] are constants, so we can add them together:
[tex]\[ 6.2 + 8.7 = 14.9 \][/tex]
Thus, the original expression simplifies to:
[tex]\[ 8.9x + 14.9 \][/tex]
Now, we need to compare each of the given expressions to this simplified form [tex]\(8.9x + 14.9\)[/tex] and see which ones are equivalent:
1. [tex]\(9x + 6 + 9\)[/tex]: Simplify the expression [tex]\(6 + 9\)[/tex] to get [tex]\(15\)[/tex], so this becomes [tex]\(9x + 15\)[/tex]. It is not the same as [tex]\(8.9x + 14.9\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]: This expression rearranges to [tex]\(8.7x + 8.9 + 6.2\)[/tex], which simplifies to [tex]\(8.7x + 15.1\)[/tex], not the same as [tex]\(8.9x + 14.9\)[/tex].
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]: This is the same as the original expression setup, and simplifies to [tex]\(8.9x + (8.7 + 6.2)\)[/tex] or [tex]\(8.9x + 14.9\)[/tex]. This is equivalent.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: Rearranging gives [tex]\(8.9x + (8.7 + 6.2)\)[/tex], which simplifies to [tex]\(8.9x + 14.9\)[/tex]. This is equivalent.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]: Simplify [tex]\(6.2 + 8.7 = 14.9\)[/tex], leading to just a constant [tex]\(14.9\)[/tex], so it doesn’t match [tex]\(8.9x + 14.9\)[/tex].
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]: Rearranging [tex]\(8.9x + (6.2 + 8.7)\)[/tex] simplifies to [tex]\(8.9x + 14.9\)[/tex]. This is equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]: This is [tex]\(6.2x + (8.9 + 8.7)\)[/tex] or [tex]\(6.2x + 17.6\)[/tex], which is not the same as [tex]\(8.9x + 14.9\)[/tex].
After analyzing each expression, the ones 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]
Here is the original expression:
[tex]\[ 8.9x + 6.2 + 8.7 \][/tex]
First, we can simplify this expression by combining like terms. Notice that [tex]\(6.2\)[/tex] and [tex]\(8.7\)[/tex] are constants, so we can add them together:
[tex]\[ 6.2 + 8.7 = 14.9 \][/tex]
Thus, the original expression simplifies to:
[tex]\[ 8.9x + 14.9 \][/tex]
Now, we need to compare each of the given expressions to this simplified form [tex]\(8.9x + 14.9\)[/tex] and see which ones are equivalent:
1. [tex]\(9x + 6 + 9\)[/tex]: Simplify the expression [tex]\(6 + 9\)[/tex] to get [tex]\(15\)[/tex], so this becomes [tex]\(9x + 15\)[/tex]. It is not the same as [tex]\(8.9x + 14.9\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]: This expression rearranges to [tex]\(8.7x + 8.9 + 6.2\)[/tex], which simplifies to [tex]\(8.7x + 15.1\)[/tex], not the same as [tex]\(8.9x + 14.9\)[/tex].
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]: This is the same as the original expression setup, and simplifies to [tex]\(8.9x + (8.7 + 6.2)\)[/tex] or [tex]\(8.9x + 14.9\)[/tex]. This is equivalent.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: Rearranging gives [tex]\(8.9x + (8.7 + 6.2)\)[/tex], which simplifies to [tex]\(8.9x + 14.9\)[/tex]. This is equivalent.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]: Simplify [tex]\(6.2 + 8.7 = 14.9\)[/tex], leading to just a constant [tex]\(14.9\)[/tex], so it doesn’t match [tex]\(8.9x + 14.9\)[/tex].
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]: Rearranging [tex]\(8.9x + (6.2 + 8.7)\)[/tex] simplifies to [tex]\(8.9x + 14.9\)[/tex]. This is equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]: This is [tex]\(6.2x + (8.9 + 8.7)\)[/tex] or [tex]\(6.2x + 17.6\)[/tex], which is not the same as [tex]\(8.9x + 14.9\)[/tex].
After analyzing each expression, the ones 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]
