Answer :
To solve this problem, we need to find which of the given equations have the same solution as the original equation. The original equation is:
[tex]\[ 2.3p - 10.1 = 0.01p \][/tex]
Let's evaluate each option:
1. Option 1: [tex]\( 2.3p - 10.1 = 6.4p - 4 \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side and constants to the other side:
[tex]\[
2.3p - 6.4p = -4 + 10.1
\][/tex]
Simplify:
[tex]\[
-4.1p = 6.1
\][/tex]
2. Option 2: [tex]\( 2.3p - 10.1 = 6.49p - 4 \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
2.3p - 6.49p = -4 + 10.1
\][/tex]
Simplify:
[tex]\[
-4.19p = 6.1
\][/tex]
3. Option 3: [tex]\( 230p - 1010 = 650p - 400 - p \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
230p + p - 650p = -400 + 1010
\][/tex]
Simplify:
[tex]\[
-419p = 610
\][/tex]
4. Option 4: [tex]\( 23p - 101 = 65p - 40 - p \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
23p + p - 65p = -40 + 101
\][/tex]
Simplify:
[tex]\[
-41p = 61
\][/tex]
5. Option 5: [tex]\( 2.3p - 14.1 = 6.4p - 4 \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
2.3p - 6.4p = -4 + 14.1
\][/tex]
Simplify:
[tex]\[
-4.1p = 10.1
\][/tex]
By comparing the simplified forms, options 3 and 4 simplify into the same structure form when you account for the number scaling (as they are equivalent when considering the multiplication factor, just shifted to a larger scale). Therefore, the correct options with the same solution as the original equation are:
- Option 3
- Option 4
[tex]\[ 2.3p - 10.1 = 0.01p \][/tex]
Let's evaluate each option:
1. Option 1: [tex]\( 2.3p - 10.1 = 6.4p - 4 \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side and constants to the other side:
[tex]\[
2.3p - 6.4p = -4 + 10.1
\][/tex]
Simplify:
[tex]\[
-4.1p = 6.1
\][/tex]
2. Option 2: [tex]\( 2.3p - 10.1 = 6.49p - 4 \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
2.3p - 6.49p = -4 + 10.1
\][/tex]
Simplify:
[tex]\[
-4.19p = 6.1
\][/tex]
3. Option 3: [tex]\( 230p - 1010 = 650p - 400 - p \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
230p + p - 650p = -400 + 1010
\][/tex]
Simplify:
[tex]\[
-419p = 610
\][/tex]
4. Option 4: [tex]\( 23p - 101 = 65p - 40 - p \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
23p + p - 65p = -40 + 101
\][/tex]
Simplify:
[tex]\[
-41p = 61
\][/tex]
5. Option 5: [tex]\( 2.3p - 14.1 = 6.4p - 4 \)[/tex]
Move terms involving [tex]\( p \)[/tex] to one side:
[tex]\[
2.3p - 6.4p = -4 + 14.1
\][/tex]
Simplify:
[tex]\[
-4.1p = 10.1
\][/tex]
By comparing the simplified forms, options 3 and 4 simplify into the same structure form when you account for the number scaling (as they are equivalent when considering the multiplication factor, just shifted to a larger scale). Therefore, the correct options with the same solution as the original equation are:
- Option 3
- Option 4
