Answer :
We begin with the equation
[tex]$$
\frac{1}{4} + s = \frac{18}{20}.
$$[/tex]
### Part A: Discussion on Possible Values for [tex]\( s \)[/tex]
This is a linear equation in one variable, which means it will have a unique solution for [tex]\( s \)[/tex]. In other words, there is exactly one value of [tex]\( s \)[/tex] that satisfies the equation.
### Part B: Solving for [tex]\( s \)[/tex]
1. Isolate [tex]\( s \)[/tex]:
Subtract [tex]\( \frac{1}{4} \)[/tex] from both sides of the equation to isolate [tex]\( s \)[/tex]:
[tex]$$
s = \frac{18}{20} - \frac{1}{4}.
$$[/tex]
2. Express with a Common Denominator:
To subtract the fractions, express [tex]\( \frac{1}{4} \)[/tex] with the same denominator as [tex]\( \frac{18}{20} \)[/tex]. Notice that
[tex]$$
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}.
$$[/tex]
3. Subtract:
Now perform the subtraction:
[tex]$$
s = \frac{18}{20} - \frac{5}{20} = \frac{18-5}{20} = \frac{13}{20}.
$$[/tex]
4. Decimal Form (Optional):
Converting [tex]\( \frac{13}{20} \)[/tex] to a decimal gives:
[tex]$$
s \approx 0.65.
$$[/tex]
### Final Answer
- Part A: [tex]\( s \)[/tex] has a unique value (or a unique solution).
- Part B: The solution is
[tex]$$
s = \frac{13}{20} \quad \text{or} \quad s \approx 0.65.
$$[/tex]
[tex]$$
\frac{1}{4} + s = \frac{18}{20}.
$$[/tex]
### Part A: Discussion on Possible Values for [tex]\( s \)[/tex]
This is a linear equation in one variable, which means it will have a unique solution for [tex]\( s \)[/tex]. In other words, there is exactly one value of [tex]\( s \)[/tex] that satisfies the equation.
### Part B: Solving for [tex]\( s \)[/tex]
1. Isolate [tex]\( s \)[/tex]:
Subtract [tex]\( \frac{1}{4} \)[/tex] from both sides of the equation to isolate [tex]\( s \)[/tex]:
[tex]$$
s = \frac{18}{20} - \frac{1}{4}.
$$[/tex]
2. Express with a Common Denominator:
To subtract the fractions, express [tex]\( \frac{1}{4} \)[/tex] with the same denominator as [tex]\( \frac{18}{20} \)[/tex]. Notice that
[tex]$$
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}.
$$[/tex]
3. Subtract:
Now perform the subtraction:
[tex]$$
s = \frac{18}{20} - \frac{5}{20} = \frac{18-5}{20} = \frac{13}{20}.
$$[/tex]
4. Decimal Form (Optional):
Converting [tex]\( \frac{13}{20} \)[/tex] to a decimal gives:
[tex]$$
s \approx 0.65.
$$[/tex]
### Final Answer
- Part A: [tex]\( s \)[/tex] has a unique value (or a unique solution).
- Part B: The solution is
[tex]$$
s = \frac{13}{20} \quad \text{or} \quad s \approx 0.65.
$$[/tex]
