Question

If y ≠ z , what are the real values of x that make the following inequality true?

(xy-xz)/3y-3z <0
A. All negative real numbers
B. All positive real numbers
C. - 1/3 only
D. 1/3 only E. 3 only

Answer 1

To solve the inequality (xy-xz)/3y-3z < 0, we can cancel out the common factor (y-z) from the numerator and denominator to get x/3 < 0. The values of x that make this inequality true are all negative real numbers.

Step-by-step explanation:

To solve the inequality, (xy-xz)/3y-3z < 0, we can start by factoring out common terms. The numerator can be factored as x(y-z), and the denominator can be factored as 3(y-z). So, the inequality becomes x(y-z)/3(y-z) < 0.

Since y and z are not equal (y ≠ z), we can cancel out the common factor (y-z) from the numerator and denominator to get x/3 < 0.

To find the values of x that make this inequality true, we need to look at the sign of x and the constant term 3.

If x is negative and 3 is positive, then x/3 will be negative. So, the answer is All negative real numbers.