Answer :
Let's verify each given value to check whether it solves the specific equations correctly.
### (a) Verify if [tex]\( x = 2 \)[/tex] is a solution to [tex]\( 2x + 4 = 15 \)[/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ 2(2) + 4 = 4 + 4 = 8 \][/tex]
Since [tex]\( 8 \neq 15 \)[/tex]:
[tex]\[ x = 2 \text{ is not a solution.} \][/tex]
### (b) Verify if [tex]\( x = 2 \)[/tex] is a solution to [tex]\( 7x + 15 = 45 \)[/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ 7(2) + 15 = 14 + 15 = 29 \][/tex]
Since [tex]\( 29 \neq 45 \)[/tex]:
[tex]\[ x = 2 \text{ is not a solution.} \][/tex]
### (c) Verify if [tex]\( x = 5 \)[/tex] is a solution to [tex]\( 7x + 2 = 23 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ 7(5) + 2 = 35 + 2 = 37 \][/tex]
Since [tex]\( 37 \neq 23 \)[/tex]:
[tex]\[ x = 5 \text{ is not a solution.} \][/tex]
### (d) Verify if [tex]\( x = 3 \)[/tex] is a solution to [tex]\( \frac{4x}{5} + 2 = 6 \)[/tex]
Substitute [tex]\( x = 3 \)[/tex]:
[tex]\[ \frac{4(3)}{5} + 2 = \frac{12}{5} + 2 = 2.4 + 2 = 4.4 \][/tex]
Since [tex]\( 4.4 \neq 6 \)[/tex]:
[tex]\[ x = 3 \text{ is not a solution.} \][/tex]
### (e) Verify if [tex]\( p = 5 \)[/tex] is a solution to [tex]\( 4p - 5 = 16 \)[/tex]
Substitute [tex]\( p = 5 \)[/tex]:
[tex]\[ 4(5) - 5 = 20 - 5 = 15 \][/tex]
Since [tex]\( 15 \neq 16 \)[/tex]:
[tex]\[ p = 5 \text{ is not a solution.} \][/tex]
### (f) Verify if [tex]\( p = 7 \)[/tex] is a solution to [tex]\( 4p - 5 = 23 \)[/tex]
Substitute [tex]\( p = 7 \)[/tex]:
[tex]\[ 4(7) - 5 = 28 - 5 = 23 \][/tex]
Since [tex]\( 23 = 23 \)[/tex]:
[tex]\[ p = 7 \text{ is a solution.} \][/tex]
### (g) Verify if [tex]\( p = 7 \)[/tex] is a solution to [tex]\( 2x + 5 = 15 \)[/tex]
Substitute [tex]\( p = 7 \)[/tex]:
[tex]\[ 2(7) + 5 = 14 + 5 = 19 \][/tex]
Since [tex]\( 19 \neq 15 \)[/tex]:
[tex]\[ p = 7 \text{ is not a solution.} \][/tex]
### (h) Verify if [tex]\( x = 5 \)[/tex] is a solution to [tex]\( 3x - 4 = 16 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ 3(5) - 4 = 15 - 4 = 11 \][/tex]
Since [tex]\( 11 \neq 16 \)[/tex]:
[tex]\[ x = 5 \text{ is not a solution.} \][/tex]
### (i) Verify if [tex]\( x = 5 \)[/tex] is a solution to [tex]\( \frac{2x}{5} + 4 = 10 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ \frac{2(5)}{5} + 4 = \frac{10}{5} + 4 = 2 + 4 = 6 \][/tex]
Since [tex]\( 6 \neq 10 \)[/tex]:
[tex]\[ x = 5 \text{ is not a solution.} \][/tex]
### Summary of Solutions:
- (a) [tex]\( x = 2 \)[/tex] is not a solution.
- (b) [tex]\( x = 2 \)[/tex] is not a solution.
- (c) [tex]\( x = 5 \)[/tex] is not a solution.
- (d) [tex]\( x = 3 \)[/tex] is not a solution.
- (e) [tex]\( p = 5 \)[/tex] is not a solution.
- (f) [tex]\( p = 7 \)[/tex] is a solution.
- (g) [tex]\( p = 7 \)[/tex] is not a solution.
- (h) [tex]\( x = 5 \)[/tex] is not a solution.
- (i) [tex]\( x = 5 \)[/tex] is not a solution.
### (a) Verify if [tex]\( x = 2 \)[/tex] is a solution to [tex]\( 2x + 4 = 15 \)[/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ 2(2) + 4 = 4 + 4 = 8 \][/tex]
Since [tex]\( 8 \neq 15 \)[/tex]:
[tex]\[ x = 2 \text{ is not a solution.} \][/tex]
### (b) Verify if [tex]\( x = 2 \)[/tex] is a solution to [tex]\( 7x + 15 = 45 \)[/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ 7(2) + 15 = 14 + 15 = 29 \][/tex]
Since [tex]\( 29 \neq 45 \)[/tex]:
[tex]\[ x = 2 \text{ is not a solution.} \][/tex]
### (c) Verify if [tex]\( x = 5 \)[/tex] is a solution to [tex]\( 7x + 2 = 23 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ 7(5) + 2 = 35 + 2 = 37 \][/tex]
Since [tex]\( 37 \neq 23 \)[/tex]:
[tex]\[ x = 5 \text{ is not a solution.} \][/tex]
### (d) Verify if [tex]\( x = 3 \)[/tex] is a solution to [tex]\( \frac{4x}{5} + 2 = 6 \)[/tex]
Substitute [tex]\( x = 3 \)[/tex]:
[tex]\[ \frac{4(3)}{5} + 2 = \frac{12}{5} + 2 = 2.4 + 2 = 4.4 \][/tex]
Since [tex]\( 4.4 \neq 6 \)[/tex]:
[tex]\[ x = 3 \text{ is not a solution.} \][/tex]
### (e) Verify if [tex]\( p = 5 \)[/tex] is a solution to [tex]\( 4p - 5 = 16 \)[/tex]
Substitute [tex]\( p = 5 \)[/tex]:
[tex]\[ 4(5) - 5 = 20 - 5 = 15 \][/tex]
Since [tex]\( 15 \neq 16 \)[/tex]:
[tex]\[ p = 5 \text{ is not a solution.} \][/tex]
### (f) Verify if [tex]\( p = 7 \)[/tex] is a solution to [tex]\( 4p - 5 = 23 \)[/tex]
Substitute [tex]\( p = 7 \)[/tex]:
[tex]\[ 4(7) - 5 = 28 - 5 = 23 \][/tex]
Since [tex]\( 23 = 23 \)[/tex]:
[tex]\[ p = 7 \text{ is a solution.} \][/tex]
### (g) Verify if [tex]\( p = 7 \)[/tex] is a solution to [tex]\( 2x + 5 = 15 \)[/tex]
Substitute [tex]\( p = 7 \)[/tex]:
[tex]\[ 2(7) + 5 = 14 + 5 = 19 \][/tex]
Since [tex]\( 19 \neq 15 \)[/tex]:
[tex]\[ p = 7 \text{ is not a solution.} \][/tex]
### (h) Verify if [tex]\( x = 5 \)[/tex] is a solution to [tex]\( 3x - 4 = 16 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ 3(5) - 4 = 15 - 4 = 11 \][/tex]
Since [tex]\( 11 \neq 16 \)[/tex]:
[tex]\[ x = 5 \text{ is not a solution.} \][/tex]
### (i) Verify if [tex]\( x = 5 \)[/tex] is a solution to [tex]\( \frac{2x}{5} + 4 = 10 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex]:
[tex]\[ \frac{2(5)}{5} + 4 = \frac{10}{5} + 4 = 2 + 4 = 6 \][/tex]
Since [tex]\( 6 \neq 10 \)[/tex]:
[tex]\[ x = 5 \text{ is not a solution.} \][/tex]
### Summary of Solutions:
- (a) [tex]\( x = 2 \)[/tex] is not a solution.
- (b) [tex]\( x = 2 \)[/tex] is not a solution.
- (c) [tex]\( x = 5 \)[/tex] is not a solution.
- (d) [tex]\( x = 3 \)[/tex] is not a solution.
- (e) [tex]\( p = 5 \)[/tex] is not a solution.
- (f) [tex]\( p = 7 \)[/tex] is a solution.
- (g) [tex]\( p = 7 \)[/tex] is not a solution.
- (h) [tex]\( x = 5 \)[/tex] is not a solution.
- (i) [tex]\( x = 5 \)[/tex] is not a solution.
