Line graph for the following equations.
8x less than 4x + 28
-5 (x+5) greater than -15
1/4 (8x +16) greater than -4
-3(x-12) greater than 0
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.
Sure! Let's solve each equation step-by-step and plot the corresponding line graphs.
1) 8x less than 4x + 28
To solve this equation, we can start by rearranging it:
8x < 4x + 28
Next, let's isolate x by subtracting 4x from both sides:
8x - 4x < 4x - 4x + 28
Simplifying further:
4x < 28
To find the value of x, divide both sides by 4:
x < 7
Now, let's plot the line graph for this inequality on a number line:
----------------------------
|
(-∞, 7) |
----------------------------
2) -5(x + 5) greater than -15
Let's solve this inequality step-by-step:
-5(x + 5) > -15
First, distribute -5 to the terms inside the parentheses:
-5x - 25 > -15
Next, add 25 to both sides to isolate x:
-5x - 25 + 25 > -15 + 25
Simplifying:
-5x > 10
To find the value of x, divide both sides by -5 (remember to flip the inequality sign when dividing by a negative number):
x < -2
Now, let's plot the line graph for this inequality on a number line:
----------------------------
|
(-∞, -2) |
----------------------------
3) (1/4)(8x + 16) greater than -4
Let's solve this inequality step-by-step:
(1/4)(8x + 16) > -4
First, distribute (1/4) to the terms inside the parentheses:
2x + 4 > -4
Next, subtract 4 from both sides to isolate x:
2x + 4 - 4 > -4 - 4
Simplifying:
2x > -8
To find the value of x, divide both sides by 2:
x > -4
Now, let's plot the line graph for this inequality on a number line:
----------------------------
|
(-4, ∞) |
----------------------------
4) -3(x - 12) greater than 0
Let's solve this inequality step-by-step:
-3(x - 12) > 0
First, distribute -3 to the terms inside the parentheses:
-3x + 36 > 0
Next, subtract 36 from both sides to isolate x:
-3x + 36 - 36 > 0 - 36
Simplifying:
-3x > -36
To find the value of x, divide both sides by -3 (remember to flip the inequality sign when dividing by a negative number):
x < 12
Now, let's plot the line graph for this inequality on a number line:
----------------------------
|
(-∞, 12) |
----------------------------
I have plotted the line graphs for each equation on a number line based on the solutions we obtained. If you have any further questions, feel free to ask!