Does an inequality of the
form ax > b always, sometimes, or never give a
solution of the form x > c? Give examples to support your answer.
looks like a typo, where is c ?
It's not a typo, that's exactly how the question was asked.
Only true if a > 0.
If a<0, then you have x < b/a or x<c.
To determine if an inequality of the form ax > b gives a solution of the form x > c, we need to consider the values of a, b, and c. Let's break down the possibilities:
1. Case where a and b are positive:
If a and b are both positive, and the inequality is ax > b, it will always give a solution of the form x > c. For example, let's take a = 3 and b = 2. In this case, the inequality 3x > 2 has a solution of the form x > 2/3.
2. Case where a and b are negative:
If a and b are both negative, and the inequality is ax > b, it will never give a solution of the form x > c. In this case, multiplying both sides of the inequality by a negative number would change the direction of the inequality. For example, if a = -4 and b = -3, then the inequality -4x > -3 would change to 4x < 3, which does not have a solution of the form x > c.
3. Case where a is positive and b is negative:
If a is positive and b is negative, the inequality ax > b can sometimes give a solution of the form x > c. However, this depends on the specific values of a and b. For example, let's take a = 2 and b = -5. In this case, the inequality 2x > -5 has a solution of the form x > -5/2.
Thus, the inequality of the form ax > b can always, sometimes, or never give a solution of the form x > c, depending on the signs and values of a and b.