Rewrite the expression without using the absolute value symbol. abs(3x-5) if x>= 5/3

vestirme4

vestirme4

Answered question

2021-03-07

Rewrite the expression without using the absolute value symbol.
|3x5| if x53

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-03-08Added 91 answers

Step 1
The expression inside the absolute value is (3x-5).
The absolute value of a number, a, is equal to the distance that a is from zero.
|a|=a,ifa0
=-(a), if a < 0
In the original definition for absolute value, replace each occurrence of a with (3x-5).
|3x5|=3x5, if 3x50
=-(3x-5), if 3x-5<0
Step 2
if x53, then |3x5|=3x5.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-11Added 2605 answers

Answer is given below (on video)

Eliza Beth13

Eliza Beth13

Skilled2023-05-12Added 130 answers

To rewrite the expression |3x5| without using the absolute value symbol, when x53, we can represent it using a piecewise function.
We know that 3x5 is positive or zero when x53. Therefore, the expression |3x5| can be written as:
|3x5|={3x5,if x53(3x5),if x<53
This notation represents the two cases when x is greater than or equal to 53 and when x is less than 53. In the first case, the absolute value of 3x5 is simply 3x5, and in the second case, it is (3x5), which is equivalent to 3x+5.
Therefore, when x53, the expression |3x5| can be rewritten as 3x5.
Don Sumner

Don Sumner

Skilled2023-05-12Added 184 answers

Result:
3x5
Solution:
To rewrite the expression |3x-5| without using the absolute value symbol, we need to consider the given condition that x ≥ 5/3.
When x ≥ 5/3, the expression 3x-5 will always be non-negative. Therefore, we can rewrite |3x-5| as simply (3x-5) without changing its value.
Hence, the expression |3x-5|, when x ≥ 5/3, can be written as:
3x5
madeleinejames20

madeleinejames20

Skilled2023-05-12Added 165 answers

We can start by noting that when x53, the expression 3x5 is non-negative. In other words, 3x50. Therefore, we can rewrite |3x5| as follows:
|3x5|={3x5,if 3x50(3x5),if 3x5<0
Since 3x5 is non-negative when x53, we can simplify the above expression as:
|3x5|=3x5
Therefore, the expression |3x5| can be rewritten as 3x5 when x53.

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