Let's solve the given equations step-by-step:
### Part (d): Solving the equation [tex]\( -7.43 - (x + 2) + 21 = 47 \)[/tex]
1. Start with the original equation:
[tex]\[
-7.43 - (x + 2) + 21 = 47
\][/tex]
2. Distribute the negative sign inside the parentheses:
[tex]\[
-7.43 - x - 2 + 21 = 47
\][/tex]
3. Combine the like terms on the left side of the equation:
[tex]\[
-7.43 - 2 + 21 = 11.57 \quad \text{(because } -7.43 - 2 = -9.43 + 21 = 11.57)
\][/tex]
So the equation becomes:
[tex]\[
11.57 - x = 47
\][/tex]
4. Subtract 11.57 from both sides of the equation to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
11.57 - x - 11.57 = 47 - 11.57
\][/tex]
Simplifying the right side results in:
[tex]\[
-x = 35.43
\][/tex]
5. To solve for [tex]\( x \)[/tex], multiply both sides by -1:
[tex]\[
x = -35.43
\][/tex]
So, the solution for part (d) is:
[tex]\[
x_d = -35.43
\][/tex]
### Part (e): Solving the equation [tex]\( 2x + 37 = 79 - 14 \)[/tex]
1. Simplify the right side of the equation:
[tex]\[
79 - 14 = 65
\][/tex]
So the equation becomes:
[tex]\[
2x + 37 = 65
\][/tex]
2. Subtract 37 from both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
2x + 37 - 37 = 65 - 37
\][/tex]
Simplifying the right side results in:
[tex]\[
2x = 28
\][/tex]
3. To solve for [tex]\( x \)[/tex], divide both sides by 2:
[tex]\[
x = \frac{28}{2} = 14
\][/tex]
So, the solution for part (e) is:
[tex]\[
x_e = 14
\][/tex]
### Part (f): Evaluating the expression [tex]\( 32 + (2 \cdot x) \)[/tex]
1. Assuming the expression should be [tex]\( 32 + (2 \cdot x) \)[/tex] and using the value of [tex]\( x \)[/tex] from part (e), which is [tex]\( x = 14 \)[/tex]:
[tex]\[
32 + (2 \cdot x) = 32 + (2 \cdot 14)
\][/tex]
2. Simplify the expression:
[tex]\[
32 + 28 = 60
\][/tex]
So, the result for part (f) is:
[tex]\[
\text{result}_f = 60
\][/tex]
### Summary:
- [tex]\( x_d = -35.43 \)[/tex]
- [tex]\( x_e = 14 \)[/tex]
- [tex]\(\text{result}_f = 60 \)[/tex]
