Answer:
x = - 6 or x = 2
Step-by-step explanation:
The absolute value function always returns a positive value. However, the expression inside can be positive or negative.
Given
| 2x + 4 | - 1 = 7 ( add 1 to both sides )
| 2x + 4 | = 8, thus
2x + 4 = 8 ( subtract 4 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
OR
-(2x + 4) = 8
- 2x - 4 = 8 ( add 4 to both sides )
- 2x = 12 ( divide both sides by - 2 )
x = - 6
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 2 → | 4 + 4 | - 1 = | 8 | - 1 = 8 - 1 = 7 ← True
x = - 6 → | - 12 + 4 | - 1 = | - 8 | - 1 = 8 - 1 = 7 ← True
Hence the solutions are x = - 6 or x = 2
Answer:
linear
Step-by-step explanation:
Answer:
4 hours
Step-by-step explanation:
We know the following:
Total amount Randy earned: $667
Pay for first 40 hours: $14.50 per hour
Pay after 40 hours: $21.75 per hour
We need to find the total extra hours: 
If the total number of hours worked are, 
, then: 
Total pay received for the first 40 hours: 
If out of $667, Randy earns $580 from the first 40 hours, the left over are earned by extra hours.
$667 - $580 = $87 ------- (a)
Total pay received for working after 40 hours: 
We know from eq (a) that total pay is 87, hence we can find the number of hours using this.
Randy worked 4 extra hours.
Answer:
Divide 63/9=7
7*2= (the number of teachers) 14
There are 14 teachers for 63 students.
<span>The tortoise crawls the whole 1000 m at 0.2 m/s, therefore, you must divide the distance by the rate of travel to find the time it took to complete the race. This gives us a time of 5,000 seconds to crawl the thousand meters. The hare runs the first 200 meters at 2 m/s, meaning that takes 100 seconds. The last 800 meters divided by the speed of 3 m/s gives us a time of 266 seconds. These two numbers must be added to the hare's rest time, converted from 1.3 hours into seconds by multiplying that number by 60 (for minutes in an hour) then 60 again (for seconds in a minute). 1.3 hours is equal to 4680 seconds. Therefore, the whole race took the hare 5,046 seconds, making it slightly slower than the hare, who finished in 5,000 seconds flat.</span>
