This is a modulus inequality.
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3
Second part: when (6x + 2) is negative.
-(6x + 2) < 10 Divide both sides of inequality by -1 and change the sign.
(6x + 2) > -10
6x + 2 > -10
6x > -10 - 2
6x > -12 Divide both sides by 6.
x > -12/6
x > -2.
Combined solution: x < 4/3 and x > -2
-2 < x < 4/3.
Graph is a line on the number line between -2 and 4/3.
-2 and 4/3 are excluded from solution.
Answer:
boys
Step-by-step explanation:
Let 
= total number of ninth graders. By knowing how many students there are in the grade, we can find for the number of boys.
(number of girls in ninth grade)
To find for the number of boys, we can use substitution:
∴ There are boys in the class.
Hope this helps :)
Try to divide by each prime number starting with 2. If it is divisible, keep trying the same prime number until it is not divisible. Then move on to the next prime number, 3. Keep dividing until you get 1. All the prime numbers you divided by are the prime factorization.
List of the first several prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Start with 85.
85 is not divisible by 2.
Move on to 3.
85 is not divisible by 3.
Move on to 5.
85/5 = 17
17 is a prime number, so now divide 17 by 17.
17/17 = 1
We divided just by 5 and 17.
Answer: The prime factors of 85 are 5 and 17.
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
Answer:
1.333 repeated
Step-by-step explanation:
