Line graph for the following equations.

Question

8x less than 4x + 28
-5 (x+5) greater than -15
1/4 (8x +16) greater than -4
-3(x-12) greater than 0

Answer 1

To graph these equations on a line graph, we need to plot the points where each equation is true and shade the region that satisfies the inequality.

1) 8x less than 4x + 28
To solve this equation, we need to move all terms involving x to one side and simplify.
8x < 4x + 28
8x - 4x < 4x - 4x + 28
4x < 28
x < 7

2) -5 (x+5) greater than -15
Again, we need to move all terms involving x to one side and simplify.
-5 (x+5) > -15
-5x - 25 > -15
-5x - 25 + 25 > -15 + 25
-5x > 10
x < -2

3) 1/4 (8x +16) greater than -4
We will move all terms involving x to one side and simplify.
1/4 (8x +16) > -4
2x + 4 > -4
2x + 4 - 4 > -4 - 4
2x > -8
x > -4

4) -3(x-12) greater than 0
Just like before, we need to simplify the equation.
-3(x-12) > 0
-3x + 36 > 0
-3x + 36 - 36 > 0 - 36
-3x > -36
x < 12

Now let's plot them on a line graph.

On the x-axis, we have the values from -10 to 20.
For the first equation (8x less than 4x + 28), we plot all real numbers less than 7. This means, we shade everything to the left of x = 7.
For the second equation (-5 (x+5) greater than -15), we plot all real numbers less than -2. This means, we shade everything to the left of x = -2.
For the third equation (1/4 (8x +16) greater than -4), we plot all real numbers greater than -4. This means, we shade everything to the right of x = -4.
For the fourth equation (-3(x-12) greater than 0), we plot all real numbers less than 12. This means, we shade everything to the left of x = 12.

I apologize, but as a text-based AI, I am unable to draw a line graph. However, I have provided the instructions for shading the regions on the graph based on the inequalities given.