Write then solve the inequality.
1. nine more than half the number n is no more than -8. Find n.
2. Judith drove h hours at a rate of 55 mi/hr. She did not reach her goal of driving 385 miles for a day. How long did she drive?
1.) 9 more than 1/2 the number no more than -8.
n = number
n + 9 = nine more
1/2 n = half the number
no more than -8 (means) <= -8
1/2 n + 9 <= -8
1/2 n <= -17
Multiply both sides by 2
n <= -34
number is 34 (less than or equal -34)
2.) h hours at rate of 55 mi/hr
D = RT (Distance = Rate x Time)
h = hours
55h = h hours at 55 mph
Did not reach goal of 385 (means) < 385
55h < 385
h < 7
Drove 7 hours (less than 7 hours)
jenny drove for 5 hours at 55 mph. how far did she drive?
1. To solve the inequality "nine more than half the number n is no more than -8," we can set up the inequality and solve for n.
The inequality is: (1/2)n + 9 ≤ -8
To solve for n, we can follow these steps:
Step 1: Subtract 9 from both sides of the inequality:
(1/2)n ≤ -17
Step 2: Multiply both sides of the inequality by 2 to get rid of the fraction:
n ≤ -34
Therefore, the solution to the inequality is n ≤ -34.
2. To find the time Judith drove, we can use the formula distance = rate × time. Given that she drove at a rate of 55 mi/hr and her goal was to drive 385 miles, we can set up the equation:
distance = rate × time
385 = 55h
To solve for h (the time she drove), we divide both sides of the equation by 55:
(385/55) = h
Simplifying further:
7 = h
Therefore, Judith drove for 7 hours.