how do you determine the domain of the variable in the expression x-6 over 5-x?
Can the denominator be zero in any math fraction? When is (5-x) zero?
To determine the domain of the variable in the expression (x - 6)/(5 - x), we need to consider the values of x that make the expression well-defined.
In this case, we have a fraction, and fractions are undefined when the denominator is equal to zero. So, we need to find the values of x for which the denominator, 5 - x, is not equal to zero.
To find this, we set 5 - x ≠ 0 and solve for x:
5 - x ≠ 0
-x ≠ -5 (subtracting 5 from both sides)
x ≠ 5 (multiplying both sides by -1 and flipping the inequality sign)
Therefore, the expression (x - 6)/(5 - x) is well-defined for all values of x except for x = 5.
Hence, the domain of the variable x is all real numbers except for x = 5.