Answer :
To solve the equation [tex]\(2.3p - 10.1 = 6.5p - 4 - 0.01p\)[/tex], we can begin by simplifying the right side. The right side becomes [tex]\(6.5p - 0.01p\)[/tex], which simplifies to [tex]\(6.49p\)[/tex]. This gives us the equation:
[tex]\[ 2.3p - 10.1 = 6.49p - 4 \][/tex]
Now, we will compare this with the options provided:
1. Option 1: [tex]\(2.3p - 10.1 = 6.4p - 4\)[/tex]
- Here, the right side is [tex]\(6.4p - 4\)[/tex].
2. Option 2: [tex]\(2.3p - 14.1 = 6.4p - 4\)[/tex]
- The left side is adjusted to [tex]\(2.3p - 14.1\)[/tex].
3. Option 3: [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]
- This matches our simplified version of the original equation.
Let's solve each of these equations to see which ones have the same solution as the original equation:
1. For the simplified original equation [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]:
- The solution is [tex]\(p = -1.45584725536993\)[/tex].
2. For Option 1 [tex]\(2.3p - 10.1 = 6.4p - 4\)[/tex]:
- The solution is [tex]\(p = -1.48780487804878\)[/tex].
3. For Option 2 [tex]\(2.3p - 14.1 = 6.4p - 4\)[/tex]:
- The solution is [tex]\(p = -2.46341463414634\)[/tex].
4. For Option 3 [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]:
- This has the same solution as the original, [tex]\(p = -1.45584725536993\)[/tex].
Based on these calculations, the equations that have the same solution as the original equation are:
- [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex] (Option 3)
This means that Option 3, [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex], is the correct answer. Another equation with the same form will also have the same solution, but only Option 3 is explicitly shown to match the solution precisely.
[tex]\[ 2.3p - 10.1 = 6.49p - 4 \][/tex]
Now, we will compare this with the options provided:
1. Option 1: [tex]\(2.3p - 10.1 = 6.4p - 4\)[/tex]
- Here, the right side is [tex]\(6.4p - 4\)[/tex].
2. Option 2: [tex]\(2.3p - 14.1 = 6.4p - 4\)[/tex]
- The left side is adjusted to [tex]\(2.3p - 14.1\)[/tex].
3. Option 3: [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]
- This matches our simplified version of the original equation.
Let's solve each of these equations to see which ones have the same solution as the original equation:
1. For the simplified original equation [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]:
- The solution is [tex]\(p = -1.45584725536993\)[/tex].
2. For Option 1 [tex]\(2.3p - 10.1 = 6.4p - 4\)[/tex]:
- The solution is [tex]\(p = -1.48780487804878\)[/tex].
3. For Option 2 [tex]\(2.3p - 14.1 = 6.4p - 4\)[/tex]:
- The solution is [tex]\(p = -2.46341463414634\)[/tex].
4. For Option 3 [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex]:
- This has the same solution as the original, [tex]\(p = -1.45584725536993\)[/tex].
Based on these calculations, the equations that have the same solution as the original equation are:
- [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex] (Option 3)
This means that Option 3, [tex]\(2.3p - 10.1 = 6.49p - 4\)[/tex], is the correct answer. Another equation with the same form will also have the same solution, but only Option 3 is explicitly shown to match the solution precisely.
