Sure, let's verify the expression [tex]\(a - (-b) = a + b\)[/tex] for the given values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
### Part (i)
Given:
[tex]\(a = -17\)[/tex]
[tex]\(b = +15\)[/tex]
Let's calculate the left-hand side (LHS) and the right-hand side (RHS) to verify the equation.
#### LHS Calculation:
[tex]\[
a - (-b) = -17 - (-15)
\][/tex]
Subtracting a negative is equivalent to adding the positive value, so:
[tex]\[
-17 - (-15) = -17 + 15
\][/tex]
#### RHS Calculation:
[tex]\[
a + b = -17 + 15
\][/tex]
Now let's perform the addition:
[tex]\[
-17 + 15 = -2
\][/tex]
So for both LHS and RHS:
[tex]\[
LHS: -17 - (-15) = -2
\][/tex]
[tex]\[
RHS: -17 + 15 = -2
\][/tex]
Since the LHS equals the RHS, the equation [tex]\( a - (-b) = a + b \)[/tex] holds true for [tex]\( a = -17 \)[/tex] and [tex]\( b = +15 \)[/tex].
### Part (ii)
Given:
[tex]\( a = 50 \)[/tex]
[tex]\( b = 21 \)[/tex]
Let's again calculate the LHS and RHS to verify the equation.
#### LHS Calculation:
[tex]\[
a - (-b) = 50 - (-21)
\][/tex]
Subtracting a negative is equivalent to adding the positive value, so:
[tex]\[
50 - (-21) = 50 + 21
\][/tex]
#### RHS Calculation:
[tex]\[
a + b = 50 + 21
\][/tex]
Now let's perform the addition:
[tex]\[
50 + 21 = 71
\][/tex]
So for both LHS and RHS:
[tex]\[
LHS: 50 - (-21) = 71
\][/tex]
[tex]\[
RHS: 50 + 21 = 71
\][/tex]
Since the LHS equals the RHS, the equation [tex]\( a - (-b) = a + b \)[/tex] holds true for [tex]\( a = 50 \)[/tex] and [tex]\( b = 21 \)[/tex].
### Conclusion
We have verified that the equation [tex]\( a - (-b) = a + b \)[/tex] is true for both pairs of given values:
1. [tex]\( a = -17 \)[/tex], [tex]\( b = +15 \)[/tex]
2. [tex]\( a = 50 \)[/tex], [tex]\( b = 21 \)[/tex]
In both cases, the left-hand side (LHS) is equal to the right-hand side (RHS), confirming the validity of the equation.
