Solve the following inequality. Graph and check your solution.
-v/2 <=6.5
Choose the correct graph below.
The correct graph is:
<graph depicting a solid line extending from positive infinity on the x-axis to -13, with a filled-in circle at -13, and shading to the left of the line>
To solve the inequality -v/2 <= 6.5, we need to isolate the variable v.
First, we can multiply both sides of the inequality by 2 to get rid of the fraction:
2 * (-v/2) <= 2 * 6.5
This simplifies to:
-v <= 13
Next, we need to multiply both sides of the inequality by -1. However, when multiplying or dividing an inequality by a negative number, we need to reverse the inequality sign. So, we have:
(-1) * (-v) >= (-1) * 13
This gives us:
v >= -13
Now, let's graph the solution on a number line.
Starting from -13, we shade all the values greater than or equal to -13, since our inequality states that v is greater than or equal to -13.
------[=======================>
-13
The arrow pointing to the right represents all the values that satisfy the inequality v >= -13.
To check our solution, we can substitute a value greater than or equal to -13 into the original inequality and see if it holds true. Let's try v = -13:
-(-13)/2 <= 6.5
13/2 <= 6.5
6.5 <= 6.5
The inequality is true when v = -13. Therefore, our solution is correct.
The correct graph is the one starting at -13 and shading all the values to the right of -13.
To solve the inequality -v/2 <= 6.5, we can start by multiplying both sides of the inequality by 2 to get rid of the fraction:
-2 * (-v/2) >= 2 * 6.5
This simplifies to:
v >= -13
Now we can graph the solution. The inequality v >= -13 represents all the values of v that are equal to or greater than -13.
To graph this on a number line, we start by plotting a closed circle at -13, indicating that -13 is included in the solution. Then, we draw an arrow to the right to show that all values greater than -13 are also part of the solution.
The correct graph representation would be an arrow pointing to the right from a closed circle at -13.
Please note that I am unable to provide a visual representation here as I am a text-based AI and cannot display images.