Question

3 questions 30 points

Answer 1

Question 12

The unknown number is: x

The question tells us that 8 fewer than a  number ( or x ) is at least 20.

The "8 fewer than a number" can also said like:   " a number minus 8 is ...)

So we know that the first part of the answer is: x - 8

For the second part, it tells us that the number minus 8  is at least 20. This can also be said like:  a number minus 8 is 20 or more (greater).

Since it is " 20 or more",  we use the  "greater than or equal to sign", which is: ≥

Answer:

Now that we know this we can say that the answer is;

x - 8 ≥ 20             (The second option)

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Question 13

So the inequality we are given to solve is:   2 < 3x -1 ≤ 5

We want to get the "3x" by itself. We do this by adding 1 to both the 2, and the 5.   Adding a 1 cancels out the -1 in  "3x - 1"   ( -1 + 1 = 0)

Alright lets do this:

2 + 1 < 3x -1 + 1 ≤ 5 + 1   =  3 < 3x ≤ 6

This is not yet finished, since we have 3x, rather than just x.  To get just x, we divide all the sides by 3 - because 3x ÷ 3 = x :

3 ÷ 3 < 3x ÷ 3 ≤ 6 ÷ 3       =   1 < x ≤ 2          (3 ÷ 3 = 1,   3x ÷ 3 = x,  and 6 ÷ 3 = 2)

Answer:  1 < x ≤ 2      (The first option)

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Question 15

The equation is:  [2x - 1] = 3

The [    ]  tells us that there are two possible answers. These are:

2x -1 = 3            or       2x -1 = -3     (negative 3)

First lets solve the one with positive three:

2x -1 = 3    ( add 1 to both sides to cancel out the -1)

2x = 4     (divide both sides by 2 to get just x)

1 < x ≤ 2

other answer with negative 3:

2x -1 = -3       ( add 1 to both sides)

2x = - 2          (  -3 + 1 = -2)

x = -1             (divide both sides by two)

Answer: So the answer is either:   x = -1   or  x = 2      (Option 2)

Answer 2

The inequality that represents the sentence is:
8-x>_20