I'll show you how to do one of the equations and one of the inequalities. All the others are done exactly in the same way: you'll only have to change the numbers, and it will be a good exercise.
Equations
Let's take the first equality as an example: we have
By definition, the absolute value of a number is the positive version of that number: if the number is already positive the absolute value doesn't change it; if a number is negative the absolute value changes its sign.
So, if the absolute value of a number is 5, than that number was already 5, or it was -5, and the absolute value changed it to positive 5.
So, the solutions are given by
Inequalities
Again, we'll use the first one as example. We have
By the same logic as before, the absolute value of a number is greater than 7 if the number is already greater than 7, or if it is smaller than -7. For example, we have |-10|=10>7.
So, we have
Instead, if we have an inequality with the "less than" sign, we have for example
Answer:
1غىخةضهاثضخ
Step-by-step explanation:
ى7غ-3ص0ض49ة=
Answer:C. 13/6
Step-by-step explanation:
The slope is always rise over run. So when going from the coordinate (-5,-7) to the coordinate (1,6) we go up 13 then go to the right 6. And since we went up and to the right it is a positive slope.
Step-by-step explanation:
Does the relationship {(1,1), (2,1),(3,2), (4,3), (5,5), (6,8), (7,13)} represent a function?
storchak [24]
Answer:
Yes.
Step-by-step explanation:
A function is a set of relations without repetitive domains.
From the given relation, there are no repetitive domains. Thus our relation here is a function.
<u>Example</u><u> </u><u>of</u><u> </u><u>Function</u>
{(1,1), (2,2), (3,3), (4,4), (5,5)}
<u>Example</u><u> </u><u>of</u><u> </u><u>Non-Function</u>
{(1,1), (1,2), (2,3), (3,4), (4,5)}
From this relation, there are two repetitive domains which are 1's. Thus not making the relation a function.
Answer:
x>−7
Step-by-step explanation:
left side:
-8(x-3)+5x
distribute -8 into (x-3)
-8x+24+5x
combine like terms
-3x+24
right side:
9(x+12)
distribute 9 into (x+12)
9x+108
-3x+24<9x+108
Subtract 24 on both sides
-3x< 9x+108-24
combine like terms
-3x<9x+84
Subtract 9x on both sides
-3x-9x<+84
combine like terms again
-12x<84
Multiply both sides by -1 (reverse the inequality)
(-12x)(-1)>84(-1)
12x>-84
divide both sides with 12
x>−7
hope this helps
