Answer :
To determine which expressions are equivalent to [tex]\(5(1.25 - 3.5x)\)[/tex], let's start by simplifying this expression:
1. Distribute the 5:
[tex]\[
5(1.25) - 5(3.5x) = 6.25 - 17.5x
\][/tex]
Now we know that the expression [tex]\(5(1.25 - 3.5x)\)[/tex] simplifies to [tex]\(6.25 - 17.5x\)[/tex]. Let's compare the given options to this simplified expression:
- Option 1: [tex]\(6.25 + 17.5x\)[/tex]
This expression is not equivalent because it has a plus sign with [tex]\(17.5x\)[/tex], whereas our expression has a minus sign with [tex]\(17.5x\)[/tex].
- Option 2: [tex]\(6.25 - 17.5x\)[/tex]
This expression is exactly the same as our simplified expression, so it is equivalent.
- Option 3: [tex]\(-17.5x - 6.25\)[/tex]
This expression rearranges the terms but changes the sign on [tex]\(6.25\)[/tex]. It doesn't match our original expression because the signs are not the same.
- Option 4: [tex]\(-17.5x + 6.25\)[/tex]
When rearranged, this expression is equivalent to [tex]\(6.25 - 17.5x\)[/tex]. The terms are simply in a different order, but the expression still represents the same values.
So, the expressions equivalent to [tex]\(5(1.25 - 3.5x)\)[/tex] are:
- [tex]\(6.25 - 17.5x\)[/tex] (Option 2)
- [tex]\(-17.5x + 6.25\)[/tex] (Option 4)
1. Distribute the 5:
[tex]\[
5(1.25) - 5(3.5x) = 6.25 - 17.5x
\][/tex]
Now we know that the expression [tex]\(5(1.25 - 3.5x)\)[/tex] simplifies to [tex]\(6.25 - 17.5x\)[/tex]. Let's compare the given options to this simplified expression:
- Option 1: [tex]\(6.25 + 17.5x\)[/tex]
This expression is not equivalent because it has a plus sign with [tex]\(17.5x\)[/tex], whereas our expression has a minus sign with [tex]\(17.5x\)[/tex].
- Option 2: [tex]\(6.25 - 17.5x\)[/tex]
This expression is exactly the same as our simplified expression, so it is equivalent.
- Option 3: [tex]\(-17.5x - 6.25\)[/tex]
This expression rearranges the terms but changes the sign on [tex]\(6.25\)[/tex]. It doesn't match our original expression because the signs are not the same.
- Option 4: [tex]\(-17.5x + 6.25\)[/tex]
When rearranged, this expression is equivalent to [tex]\(6.25 - 17.5x\)[/tex]. The terms are simply in a different order, but the expression still represents the same values.
So, the expressions equivalent to [tex]\(5(1.25 - 3.5x)\)[/tex] are:
- [tex]\(6.25 - 17.5x\)[/tex] (Option 2)
- [tex]\(-17.5x + 6.25\)[/tex] (Option 4)
