To solve the problem, we needed to find the lower bound for the value of [tex]\(4y + 1\)[/tex] given that [tex]\(y\)[/tex] is 1.8, correct to 1 decimal place. Here's the step-by-step solution:
1. Identify the value of [tex]\(y\)[/tex]:
- Given [tex]\(y = 1.8\)[/tex], correct to 1 decimal place.
2. Determine the lower bound of [tex]\(y\)[/tex]:
- Since [tex]\(y\)[/tex] is 1.8, correct to 1 decimal place, the lower bound for [tex]\(y\)[/tex] is 1.75. This is because the range for [tex]\(y\)[/tex] would be from 1.75 to just below 1.85. To represent this range:
[tex]\[
1.75 \leq y < 1.85
\][/tex]
3. Calculate [tex]\(4y + 1\)[/tex] using the lowest possible value of [tex]\(y\)[/tex]:
- Using the lower bound of [tex]\(y\)[/tex], which is 1.75, the expression [tex]\(4y + 1\)[/tex] becomes:
[tex]\[
4 \times 1.75 + 1 = 7 + 1 = 8
\][/tex]
4. Conclusion:
- Therefore, the lower bound for the value of [tex]\(4y + 1\)[/tex], given [tex]\(y = 1.8\)[/tex] correct to 1 decimal place, is 8.
Thus, the lower bound for [tex]\(4y + 1\)[/tex] is 8.
