my question is :

on the following i have to graph them i just want to know if i am correct.

for : x > 4
the line is going through in a straight line on number 4 in the y axis

for: 3x greater than or equal to 2x - 4 the answer is after solving:
x is less than or equal to -4 . this line would be strating from -4 to the left side where all the rest of negative numbers are it would be right on 0,-4.

for: 7(x-3)greater than 5x-14
my answer is : x > -1
the line would be from negative 1 meaning 0,-1 . so the line goes from 0,-1 straight across to the positive side.

Let's go through each question and determine if your answers are correct. To graph the given inequalities, we'll need to plot points on a number line.

1. For the inequality x > 4, you are correct that the line would pass through the number 4 in the y-axis. However, it is important to note that since x is greater than 4, the line would extend infinitely to the right side of the number line.

2. For the inequality 3x ≥ 2x - 4, you correctly solved it as x ≤ -4. However, when plotting this on a number line, the line should start from -4 and extend towards the left, covering all numbers less than or equal to -4. So your point (-4, 0) is correct, but the line should move towards the left side of the number line.

3. For the inequality 7(x-3) > 5x - 14, you correctly solved it as x > -1. When plotting this on a number line, you would place a dot on -1 and draw a line going towards the right side of the number line, covering all values greater than -1.

So, in summary, your answers for the first and third inequalities are correct, but there's a slight mistake in your second inequality interpretation.