Answer :
To solve the equation [tex]\(2.3p - 10.1 = 6.5p - 4 - 0.01p\)[/tex] and find which options have the same solution, we need to simplify the right side of the equation.
1. Combine like terms on the right side:
You have [tex]\(6.5p - 0.01p\)[/tex], which simplifies to [tex]\(6.49p\)[/tex]. So, the equation becomes:
[tex]\[
2.3p - 10.1 = 6.49p - 4
\][/tex]
Now let's evaluate the given options to see which equations have the same structure:
- Option 1: [tex]\(2.3p - 10.1 = 6.4p - 4\)[/tex]
This equation does not match; [tex]\(6.4p\)[/tex] is not the same as [tex]\(6.49p\)[/tex].
- Option 2: [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]
This equation matches exactly after combining the right side terms. So, this is correct.
- Option 3: [tex]\(230p - 1010 = 650p - 400 - p\)[/tex]
Let's simplify the right side: [tex]\(650p - p\)[/tex] is [tex]\(649p\)[/tex]. This does not simplify to our transformed equation.
- Option 4: [tex]\(23p - 101 = 65p - 40 - p\)[/tex]
Let's simplify the right side: [tex]\(65p - p\)[/tex] is [tex]\(64p\)[/tex]. This does not simplify to our transformed equation.
So, the correct equation that has the same solution is [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex].
1. Combine like terms on the right side:
You have [tex]\(6.5p - 0.01p\)[/tex], which simplifies to [tex]\(6.49p\)[/tex]. So, the equation becomes:
[tex]\[
2.3p - 10.1 = 6.49p - 4
\][/tex]
Now let's evaluate the given options to see which equations have the same structure:
- Option 1: [tex]\(2.3p - 10.1 = 6.4p - 4\)[/tex]
This equation does not match; [tex]\(6.4p\)[/tex] is not the same as [tex]\(6.49p\)[/tex].
- Option 2: [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]
This equation matches exactly after combining the right side terms. So, this is correct.
- Option 3: [tex]\(230p - 1010 = 650p - 400 - p\)[/tex]
Let's simplify the right side: [tex]\(650p - p\)[/tex] is [tex]\(649p\)[/tex]. This does not simplify to our transformed equation.
- Option 4: [tex]\(23p - 101 = 65p - 40 - p\)[/tex]
Let's simplify the right side: [tex]\(65p - p\)[/tex] is [tex]\(64p\)[/tex]. This does not simplify to our transformed equation.
So, the correct equation that has the same solution is [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex].
