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)