Problem 1 :
Find the absolute value of the integer -9.
Problem 2 :
Find the absolute value of the integer 9.
Problem 3 :
Find the absolute value of (-17 + 8).
Problem 4 :
Find the absolute value of (28 - 13).
Problem 5 :
If |x| is an integer between 0 and 3, then, find all possible values of x.
Problem 6 :
If |2x - 1| is an integer between 3 and 6, then, find all possible values of x.
Problem 7 :
Solve for x :
|3x + 5| = 7
Problem 8 :
Solve for x :
|7x| = 21
Problem 9 :
Solve for x :
2|3x +4| = 8
Problem 10 :
Solve for x :
3|5x - 6| - 4 = 5
Problem 1 :
Find the absolute value of the integer -9.
Solution :
|-9| = 9
Problem 2 :
Find the absolute value of the integer 9.
Solution :
|9| = 9
Problem 3 :
Find the absolute value of (-17 + 8).
Solution :
|-17 + 8| = |-9|
|-17 + 8| = 9
Problem 4 :
Find the absolute value of (28 - 13).
Solution :
|28 - 13| = |15|
|28 - 13| = 15
Problem 5 :
If |x| is an integer between 0 and 3, then, find all possible values of x.
Solution :
Given : |x| is an integer between 0 and 3.
Then, we have
|x| = 1 and |x| = 2
Solve for x in |x| = 1.
x = 1 |
x = -1 |
Solve for x in |x| = 2.
x = 2 |
x = -2 |
So, the possible values of x are
-2, -1, 1, 2
Problem 6 :
If |2x - 1| is an integer between 3 and 6, then, find all possible values of x.
Solution :
Given : |2x - 1| is an integer between 3 and 6.
Then, we have
|2x - 1| = 4 and |2x - 1| = 5
Solve for x in |2x - 1| = 4.
2x - 1 = 4 2x = 5 x = 5/2 |
2x - 1 = -4 2x = -3 x = -3/2 |
Solve for x in |2x - 1| = 5.
2x - 1 = 5 2x = 6 x = 3 |
2x - 1 = -5 2x = -4 x = -2 |
So, the possible values of x are
-2, -3/2, 5/2, 3
Problem 7 :
Solve for x :
|3x + 5| = 7
Solution :
|3x + 5| = 7
The expression inside the absolute value can be either positive or negative.
Then, we have
3x + 5 = 7 3x = 2 x = 2/3 |
3x + 5 = -7 3x = -12 x = -4 |
So, the values of x are
-4, 2/3
Problem 8 :
Solve for x :
|7x| = 21
Solution :
|7x| = 21
The expression inside the absolute value can be either positive or negative.
Then, we have
7x = 21 x = 3 |
7x = -21 x = -3 |
So, the values of x are
-3, 3
Problem 9 :
Solve for x :
2|3x +4| = 8
Solution :
2|3x +4| = 7
Divide each side by 2.
|3x + 4| = 4
The expression inside the absolute value can be either positive or negative.
Then, we have
3x + 4 = 4 3x = 0 x = 0 |
3x + 4 = -4 3x = -8 x = -8/3 |
So, the values of x are
-8/3, 0
Problem 10 :
Solve for x :
3|5x - 6| - 4 = 5
Solution :
3|5x - 6| - 4 = 5
Add 4 to each side.
3|5x - 6| = 9
Divide each side by 3.
|5x - 6| = 3
5x - 6 = 3 5x = 9 x = 9/5 |
5x - 6 = -3 5x = 3 x = 3/5 |
So, the values of x are
3/5, 9/5
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