The equation 2x + 5 has no solutions for x > -5/2, as the function is always positive and does not intersect the x-axis in this range.
The equation 2x + 5 has no solutions when the expression on the left side cannot be equal to any real number. In this case, the equation represents a linear function with a slope of 2, meaning that for every change in x by 1 unit, the corresponding change in the expression is 2 units.
To find when there are no solutions, we observe that the equation is in the form y = 2x + 5, where y is the output. Since the slope is positive, the function is monotonically increasing. Therefore, there are no solutions when the expression 2x + 5 is always greater than any real number, indicating that the function never crosses the x-axis.
Mathematically, this occurs when the slope is steeper than the negative reciprocal of the coefficient of x. In this case, the slope is steeper than -1/2. Thus, the equation has no solutions when x is in the range where 2x + 5 > 0, making x greater than -5/2.
The question probable may be:
For what values of x does the equation 2x + 5 have no solutions?