When x is divided by 3,the remainder is z.In terms of z, which of the following could be equal to x ?
a. z-3
b. 3-z
c. 3z
d. 6+z
e. 9+2z
please answer and explain
To find the possible values of x in terms of z, we need to consider the relationship between x and z when x is divided by 3.
When x is divided by 3, the remainder is z. This means that x can be expressed as:
x = 3n + z
where n is an integer.
Now let's evaluate the given options in terms of z:
a. z - 3:
If we substitute this expression into the equation x = 3n + z, we get:
x = 3n + (z - 3) = 3n + z - 3
This is a valid expression for x, so option a is possible.
b. 3 - z:
Substituting this expression into the equation x = 3n + z:
x = 3n + (3 - z) = 3n + 3 - z
This is a valid expression for x, so option b is also possible.
c. 3z:
Substituting this expression into the equation x = 3n + z:
x = 3n + 3z
This is not a valid expression for x, as there is no variable n present. Option c is not possible.
d. 6 + z:
Substituting this expression into the equation x = 3n + z:
x = 3n + (6 + z) = 3n + 6 + z
This is a valid expression for x, so option d is possible.
e. 9 + 2z:
Substituting this expression into the equation x = 3n + z:
x = 3n + (9 + 2z) = 3n + 9 + 2z
This is a valid expression for x, so option e is also possible.
Therefore, the possible values of x in terms of z are:
a. z - 3
b. 3 - z
d. 6 + z
e. 9 + 2z
So the correct options are a, b, d, and e.
To answer this question, we need to understand the concept of "divisor" and "remainder" in division.
When a number (x) is divided by another number (3 in this case), the remainder (z) is the leftover value after performing the division operation.
Now let's analyze each option:
a. z - 3: This option represents a result that is 3 units smaller than the remainder (z). It may not be equal to x because the remainder (z) is the "leftover" value and won't necessarily have a constant relationship with x.
b. 3 - z: This option represents a result that is 3 units larger than the remainder (z). Similar to option a, it may not be equal to x because the remainder (z) doesn't have a fixed relationship with x.
c. 3z: This option represents a result that is 3 times the remainder (z). Since 3 times any value will give a different result from the original value, this option is unlikely to be equal to x.
d. 6 + z: This option represents a result that is 6 units larger than the remainder (z). Since the remainder (z) could have any value, adding 6 to it would not necessarily equal x. Therefore, this option cannot be guaranteed to be equal to x.
e. 9 + 2z: This option represents a result that is 9 units larger than twice the remainder (z). Similar to the previous options, this does not guarantee that it will be equal to x.
Based on the explanations provided, none of the options (a, b, c, d, or e) can be confirmed to be equal to x. The value of x cannot be determined solely based on the given information.
You know that if the remainder is zero, x is a multiple of 3.
But, there is a remainder of z, so add that in.
Only one of the choices is a multiple of 3, with an extra z