Certainly! Let's go through each part of the question to check if the given values satisfy the equations:
### Part (a)
Given an equation:
[tex]\[ n + 5 = 19(n - 1) \][/tex]
We need to check if [tex]\( n = 1 \)[/tex] is a solution to this equation.
1. Substitute [tex]\( n = 1 \)[/tex] into the left-hand side (LHS):
[tex]\[ 1 + 5 = 6 \][/tex]
2. Substitute [tex]\( n = 1 \)[/tex] into the right-hand side (RHS):
[tex]\[ 19(1 - 1) = 19 \times 0 = 0 \][/tex]
3. Compare LHS and RHS:
[tex]\[ \text{LHS} = 6 \][/tex]
[tex]\[ \text{RHS} = 0 \][/tex]
Since 6 is not equal to 0, [tex]\( n = 1 \)[/tex] is not a solution to the equation.
### Part (b)
Given another equation:
[tex]\[ 7n + 5 = 19(n + 2) \][/tex]
We need to check if [tex]\( n = -2 \)[/tex] is a solution to this equation.
1. Substitute [tex]\( n = -2 \)[/tex] into the left-hand side (LHS):
[tex]\[ 7(-2) + 5 = -14 + 5 = -9 \][/tex]
2. Substitute [tex]\( n = -2 \)[/tex] into the right-hand side (RHS):
[tex]\[ 19(-2 + 2) = 19 \times 0 = 0 \][/tex]
3. Compare LHS and RHS:
[tex]\[ \text{LHS} = -9 \][/tex]
[tex]\[ \text{RHS} = 0 \][/tex]
Since -9 is not equal to 0, [tex]\( n = -2 \)[/tex] is not a solution to the equation.
### Summary:
- For equation [tex]\( n + 5 = 19(n - 1) \)[/tex], [tex]\( n = 1 \)[/tex] is not a solution.
- For equation [tex]\( 7n + 5 = 19(n + 2) \)[/tex], [tex]\( n = -2 \)[/tex] is not a solution.
