Absolute value is denoted by || and represents the distance from zero.
The absolute value of a positive number - will always be the number itself.
For example:
The absolute value of a negative number - will always be the same number but positive.
For example:
Note that the absolute value of a number will always be positive since distance is always positive.
If we have an unknown or an expression with an unknown inside absolute value, we ask ourselves which expression will give us the desired equation value, split into cases and find the unknown.
For example in the equation:
We ask ourselves, which expression in absolute value will equal 12.
The answer will be 12 or -12. (both 12 in absolute value equals 12 and -12 in absolute value equals 12).
Therefore, we'll take the entire expression and split it into two cases:
First case:
Let's solve:
Second case:
Let's solve:
Therefore, the solution to the exercise is:
Determine the absolute value of the following number:
\( \left|18\right|= \)
\( \left|-2\right|= \)
\( \left|3\right|= \)
\( \left|0.8\right|= \)
\( \left|x\right|= \)
Determine the absolute value of the following number:
The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.
When we have an exercise with these symbols || we understand that it refers to absolute value.
Absolute value does not relate to whether a number is positive or negative, but rather checks how far it is from zero.
In other words, 2 is 2 units away from zero, and -2 is also 2 units away from zero,
Therefore, absolute value essentially "zeroes out" the negativity of the number.
|-2| = 2
\( \left|3^2\right|= \)
\( \left|-19\frac{1}{4}\right|= \)
\( −\left|-18\right|= \)
\( -\lvert4^2\rvert= \)
Are the numbers opposite?
\( \left|-3\right|,\left|3\right| \)
Are the numbers opposite?
No
\( -\left|-y^2\right|= \)
Are the numbers opposite?
\( -\left|-81\right|,\left|9^2\right| \)
Are the numbers opposite?
\( -\left|-801\right|,\left|+801\right| \)
Are the numbers opposite?
\( \left|-\frac{1}{3}\right|,\left|\frac{3}{1}\right| \)
Are the numbers opposite?
\( \left|56\right|,\left|-5.6\right| \)
Are the numbers opposite?
Yes
Are the numbers opposite?
Yes
Are the numbers opposite?
No
Are the numbers opposite?
No