Sure! Let's solve each equation step by step.
35. [tex]\( 7p + 5 = 47 \)[/tex]
1. Subtract 5 from both sides:
[tex]\[
7p + 5 - 5 = 47 - 5
\][/tex]
This simplifies to:
[tex]\[
7p = 42
\][/tex]
2. Divide both sides by 7:
[tex]\[
\frac{7p}{7} = \frac{42}{7}
\][/tex]
This gives us:
[tex]\[
p = 6
\][/tex]
36. [tex]\( 2q - 7 = 31 \)[/tex]
1. Add 7 to both sides:
[tex]\[
2q - 7 + 7 = 31 + 7
\][/tex]
This simplifies to:
[tex]\[
2q = 38
\][/tex]
2. Divide both sides by 2:
[tex]\[
\frac{2q}{2} = \frac{38}{2}
\][/tex]
This gives us:
[tex]\[
q = 19
\][/tex]
37. [tex]\( \frac{e}{5} - 6 = -9 \)[/tex]
1. Add 6 to both sides:
[tex]\[
\frac{e}{5} - 6 + 6 = -9 + 6
\][/tex]
This simplifies to:
[tex]\[
\frac{e}{5} = -3
\][/tex]
2. Multiply both sides by 5:
[tex]\[
5 \cdot \frac{e}{5} = 5 \cdot (-3)
\][/tex]
This gives us:
[tex]\[
e = -15
\][/tex]
38. [tex]\( \frac{d}{3} + 4 = 1 \)[/tex]
1. Subtract 4 from both sides:
[tex]\[
\frac{d}{3} + 4 - 4 = 1 - 4
\][/tex]
This simplifies to:
[tex]\[
\frac{d}{3} = -3
\][/tex]
2. Multiply both sides by 3:
[tex]\[
3 \cdot \frac{d}{3} = 3 \cdot (-3)
\][/tex]
This gives us:
[tex]\[
d = -9
\][/tex]
So, the solutions are:
- [tex]\( p = 6 \)[/tex]
- [tex]\( q = 19 \)[/tex]
- [tex]\( e = -15 \)[/tex]
- [tex]\( d = -9 \)[/tex]
