Sure, let's work through each of these expressions step-by-step.
### Part (a) [tex]\( 8m - 5 \)[/tex] when [tex]\( m = -2 \)[/tex]
1. Substitute [tex]\( m \)[/tex] with [tex]\(-2\)[/tex] in the expression [tex]\( 8m - 5 \)[/tex].
2. This gives us:
[tex]\[
8(-2) - 5
\][/tex]
3. Multiply 8 by [tex]\(-2\)[/tex]:
[tex]\[
-16 - 5
\][/tex]
4. Subtract 5 from [tex]\(-16\)[/tex]:
[tex]\[
-16 - 5 = -21
\][/tex]
So, the value of the expression [tex]\( 8m - 5 \)[/tex] when [tex]\( m = -2 \)[/tex] is [tex]\(-21\)[/tex].
### Part (c) [tex]\( 2x + 3y \)[/tex] when [tex]\( x = 4 \)[/tex] and [tex]\( y = 5 \)[/tex]
1. Substitute [tex]\( x \)[/tex] with 4 and [tex]\( y \)[/tex] with 5 in the expression [tex]\( 2x + 3y \)[/tex].
2. This gives us:
[tex]\[
2(4) + 3(5)
\][/tex]
3. Multiply 2 by 4:
[tex]\[
8 + 3(5)
\][/tex]
4. Multiply 3 by 5:
[tex]\[
8 + 15
\][/tex]
5. Add 8 and 15:
[tex]\[
8 + 15 = 23
\][/tex]
So, the value of the expression [tex]\( 2x + 3y \)[/tex] when [tex]\( x = 4 \)[/tex] and [tex]\( y = 5 \)[/tex] is 23.
### Part (e) [tex]\( \frac{u}{2} - 5 \)[/tex] when [tex]\( u = 4 \)[/tex]
1. Substitute [tex]\( u \)[/tex] with 4 in the expression [tex]\( \frac{u}{2} - 5 \)[/tex].
2. This gives us:
[tex]\[
\frac{4}{2} - 5
\][/tex]
3. Divide 4 by 2:
[tex]\[
2 - 5
\][/tex]
4. Subtract 5 from 2:
[tex]\[
2 - 5 = -3
\][/tex]
So, the value of the expression [tex]\( \frac{u}{2} - 5 \)[/tex] when [tex]\( u = 4 \)[/tex] is [tex]\(-3\)[/tex].
Therefore, the final results for each expression are:
- [tex]\( 8m - 5 \)[/tex] when [tex]\( m = -2 \)[/tex] is [tex]\(-21\)[/tex].
- [tex]\( 2x + 3y \)[/tex] when [tex]\( x = 4 \)[/tex] and [tex]\( y = 5 \)[/tex] is 23.
- [tex]\( \frac{u}{2} - 5 \)[/tex] when [tex]\( u = 4 \)[/tex] is [tex]\(-3\)[/tex].
