For which vAlues of x the following expressions not defined if all these expressions are real numbers
1. 2x-1
negative ------
3x-2
2.square root of 2(x-7)
1. X = +- Infinity.
2. X < 7.
To determine the values of x for which the given expressions are not defined, we need to identify the restrictions or conditions that would make the expressions invalid.
1. Expression: (2x - 1) / (3x - 2)
In this case, the expression is a fraction. The denominator (3x - 2) cannot be equal to zero since division by zero is undefined. So, to find the values of x for which the expression is not defined, we solve the equation:
3x - 2 = 0
Solving for x, we have:
3x = 2
x = 2/3
Therefore, the expression (2x - 1) / (3x - 2) is not defined when x = 2/3.
2. Expression: √(2(x - 7))
Similarly, in this expression, the square root cannot be taken of a negative number. Therefore, we need to determine the values of x that would result in a negative number under the square root.
The expression inside the square root, 2(x - 7), must be greater than or equal to zero for the expression to be defined. So, we solve the inequality:
2(x - 7) ≥ 0
Expanding this inequality:
2x - 14 ≥ 0
To find the values of x, we solve the equation:
2x - 14 = 0
2x = 14
x = 14/2
x = 7
Therefore, the expression √(2(x - 7)) is defined for all values of x greater than or equal to 7.
To summarize:
1. The expression (2x - 1) / (3x - 2) is not defined for x = 2/3.
2. The expression √(2(x - 7)) is defined for x ≥ 7.