Sure, let's verify whether the given values satisfy the equations one by one.
### (a)
Equation: [tex]\( 2x + 4 = 15 \)[/tex]
Given: [tex]\( x = 2 \)[/tex]
[tex]\[
2(2) + 4 = 4 + 4 = 8
\][/tex]
The left-hand side (LHS) is 8, which does not equal the right-hand side (RHS) of 15.
Result: The value [tex]\( x = 2 \)[/tex] is not a solution to the equation.
### (b)
Equation: [tex]\( 7x + 15 = 45 \)[/tex]
Given: [tex]\( x = 5 \)[/tex]
[tex]\[
7(5) + 15 = 35 + 15 = 50
\][/tex]
The LHS is 50, which does not equal the RHS of 45.
Result: The value [tex]\( x = 5 \)[/tex] is not a solution to the equation.
### (c)
Equation: [tex]\( 7x + 2 = 23 \)[/tex]
Given: [tex]\( x = 3 \)[/tex]
[tex]\[
7(3) + 2 = 21 + 2 = 23
\][/tex]
The LHS is 23, which equals the RHS of 23.
Result: The value [tex]\( x = 3 \)[/tex] is a solution to the equation.
### (d)
Equation: [tex]\( \frac{4x}{5} + 2 = 6 \)[/tex]
Given: [tex]\( x = 5 \)[/tex]
[tex]\[
\frac{4(5)}{5} + 2 = \frac{20}{5} + 2 = 4 + 2 = 6
\][/tex]
The LHS is 6, which equals the RHS of 6.
Result: The value [tex]\( x = 5 \)[/tex] is a solution to the equation.
### (e)
Equation: [tex]\( 4p - 5 = 16 \)[/tex]
Given: [tex]\( p = 7 \)[/tex]
[tex]\[
4(7) - 5 = 28 - 5 = 23
\][/tex]
The LHS is 23, which does not equal the RHS of 16.
Result: The value [tex]\( p = 7 \)[/tex] is not a solution to the equation.
### (f)
Equation: [tex]\( 4p - 5 = 23 \)[/tex]
Given: [tex]\( p = 7 \)[/tex]
[tex]\[
4(7) - 5 = 28 - 5 = 23
\][/tex]
The LHS is 23, which equals the RHS of 23.
Result: The value [tex]\( p = 7 \)[/tex] is a solution to the equation.
### (g)
Equation: [tex]\( 2x + 5 = 15 \)[/tex]
Given: [tex]\( x = 5 \)[/tex]
[tex]\[
2(5) + 5 = 10 + 5 = 15
\][/tex]
The LHS is 15, which equals the RHS of 15.
Result: The value [tex]\( x = 5 \)[/tex] is a solution to the equation.
### (h)
Equation: [tex]\( 3x - 4 = 16 \)[/tex]
Given: [tex]\( x = 2 \)[/tex]
[tex]\[
3(2) - 4 = 6 - 4 = 2
\][/tex]
The LHS is 2, which does not equal the RHS of 16.
Result: The value [tex]\( x = 2 \)[/tex] is not a solution to the equation.
### (i)
Equation: [tex]\( \frac{2x}{5} + 4 = 10 \)[/tex]
Given: [tex]\( x = 5 \)[/tex]
[tex]\[
\frac{2(5)}{5} + 4 = \frac{10}{5} + 4 = 2 + 4 = 6
\][/tex]
The LHS is 6, which does not equal the RHS of 10.
Result: The value [tex]\( x = 5 \)[/tex] is not a solution to the equation.
