Let's solve each of these equations step-by-step:
### Part a) [tex]\(5 + a = 18\)[/tex]
To isolate [tex]\(a\)[/tex], we need to subtract 5 from both sides of the equation:
[tex]\[ a = 18 - 5 \][/tex]
So,
[tex]\[ a = 13 \][/tex]
### Part c) [tex]\(3c = 21\)[/tex]
To isolate [tex]\(c\)[/tex], we need to divide both sides of the equation by 3:
[tex]\[ c = \frac{21}{3} \][/tex]
So,
[tex]\[ c = 7 \][/tex]
### Part b) [tex]\(b - 15 = 17\)[/tex]
To isolate [tex]\(b\)[/tex], we need to add 15 to both sides of the equation:
[tex]\[ b = 17 + 15 \][/tex]
So,
[tex]\[ b = 32 \][/tex]
### Part d) [tex]\(\frac{d}{8} = 5\)[/tex]
To isolate [tex]\(d\)[/tex], we need to multiply both sides of the equation by 8:
[tex]\[ d = 5 \times 8 \][/tex]
So,
[tex]\[ d = 40 \][/tex]
### Part e) [tex]\(2e + 4 = 10\)[/tex]
To isolate [tex]\(e\)[/tex], we'll first subtract 4 from both sides of the equation:
[tex]\[ 2e = 10 - 4 \][/tex]
which simplifies to:
[tex]\[ 2e = 6 \][/tex]
Next, we'll divide both sides by 2:
[tex]\[ e = \frac{6}{2} \][/tex]
So,
[tex]\[ e = 3 \][/tex]
### Part f) [tex]\(4f - 12 = 4\)[/tex]
To isolate [tex]\(f\)[/tex], we'll first add 12 to both sides of the equation:
[tex]\[ 4f = 4 + 12 \][/tex]
which simplifies to:
[tex]\[ 4f = 16 \][/tex]
Next, we'll divide both sides by 4:
[tex]\[ f = \frac{16}{4} \][/tex]
So,
[tex]\[ f = 4 \][/tex]
### Summary
The values of the variables that make these sentences true are:
- [tex]\( a = 13 \)[/tex]
- [tex]\( c = 7 \)[/tex]
- [tex]\( b = 32 \)[/tex]
- [tex]\( d = 40 \)[/tex]
- [tex]\( e = 3 \)[/tex]
- [tex]\( f = 4 \)[/tex]
So, the final solution is:
[tex]\[
(a, c, b, d, e, f) = (13, 7, 32, 40, 3, 4)
\][/tex]
