Answer :
Let's solve the problem step by step to find out which equations correctly represent the statement:
The statement is:
"The value of 81 is 19 more than [tex]\( j \)[/tex]."
This can be translated into an equation format. When the statement says that 81 is 19 more than [tex]\( j \)[/tex], it means that if we take [tex]\( j \)[/tex] and add 19 to it, we will get 81.
This forms the equation:
[tex]\[ j + 19 = 81 \][/tex]
Let's compare this with the options given:
1. [tex]\( 81 = j - 19 \)[/tex]
This implies that 81 is equal to [tex]\( j \)[/tex] minus 19. It does not match the statement that 81 is 19 more than [tex]\( j \)[/tex].
2. [tex]\( 81 = j + 19 \)[/tex]
This implies that 81 is 19 more than [tex]\( j \)[/tex]. This correctly represents the statement.
3. [tex]\( 19 + j = 81 \)[/tex]
This is a rearrangement of the equation [tex]\( j + 19 = 81 \)[/tex] and also correctly represents the statement.
4. [tex]\( 19 \times j = 81 \)[/tex]
This suggests multiplying [tex]\( j \)[/tex] by 19 equals 81, which does not match the statement.
5. [tex]\( 81 \times j = 19 \)[/tex]
This suggests multiplying [tex]\( j \)[/tex] by 81 equals 19, which does not match the statement.
6. [tex]\( 81 \div j = 19 \)[/tex]
This implies dividing 81 by [tex]\( j \)[/tex] equals 19, which does not match the statement.
Based on this analysis, the equations that correctly represent the statement "The value of 81 is 19 more than [tex]\( j \)[/tex]" are:
- [tex]\( 81 = j + 19 \)[/tex]
- [tex]\( 19 + j = 81 \)[/tex]
These equations accurately reflect the relationship described in the statement.
The statement is:
"The value of 81 is 19 more than [tex]\( j \)[/tex]."
This can be translated into an equation format. When the statement says that 81 is 19 more than [tex]\( j \)[/tex], it means that if we take [tex]\( j \)[/tex] and add 19 to it, we will get 81.
This forms the equation:
[tex]\[ j + 19 = 81 \][/tex]
Let's compare this with the options given:
1. [tex]\( 81 = j - 19 \)[/tex]
This implies that 81 is equal to [tex]\( j \)[/tex] minus 19. It does not match the statement that 81 is 19 more than [tex]\( j \)[/tex].
2. [tex]\( 81 = j + 19 \)[/tex]
This implies that 81 is 19 more than [tex]\( j \)[/tex]. This correctly represents the statement.
3. [tex]\( 19 + j = 81 \)[/tex]
This is a rearrangement of the equation [tex]\( j + 19 = 81 \)[/tex] and also correctly represents the statement.
4. [tex]\( 19 \times j = 81 \)[/tex]
This suggests multiplying [tex]\( j \)[/tex] by 19 equals 81, which does not match the statement.
5. [tex]\( 81 \times j = 19 \)[/tex]
This suggests multiplying [tex]\( j \)[/tex] by 81 equals 19, which does not match the statement.
6. [tex]\( 81 \div j = 19 \)[/tex]
This implies dividing 81 by [tex]\( j \)[/tex] equals 19, which does not match the statement.
Based on this analysis, the equations that correctly represent the statement "The value of 81 is 19 more than [tex]\( j \)[/tex]" are:
- [tex]\( 81 = j + 19 \)[/tex]
- [tex]\( 19 + j = 81 \)[/tex]
These equations accurately reflect the relationship described in the statement.
