Solve the inequality. Graph and check your solution.
-1/5m>-2
To solve the inequality -1/5m > -2, we can multiply both sides by -5 (remember to reverse the inequality sign when multiplying by a negative number):
(-1/5m)(-5) < (-2)(-5)
m < 10
Now we can graph the solution on a number line:
On the number line, we have an open circle at 10 (since the inequality is m < 10, we do not include 10 in the solution) and the arrow pointing towards negative infinity (since m is less than 10).
To check our solution, we can pick a value less than 10, such as 5. Plugging it into the original inequality:
-1/(5*5) > -2
-1/25 > -2
This is true, so our solution is correct.
To solve the inequality -1/5m > -2, we need to isolate the variable 'm' on one side of the inequality sign.
Step 1: Multiply both sides of the inequality by -5 to eliminate the fraction:
(-5)(-1/5m) < (-5)(-2)
m < 10
Step 2: Graphing the solution:
To graph the solution, we need to plot all the values of 'm' that make the inequality true. In this case, since it is a strict inequality (m < 10), we need to represent the solution as an open circle on a number line positioned slightly to the left of the number 10. This indicates that 10 is not included in the solution set.
Step 3: Checking the solution:
To check the solution, we can substitute a value less than 10 into the original inequality and see if it holds true. Let's say we substitute m = 5:
-1/5(5) > -2
-1 > -2
This is true, so our solution m < 10 is valid.
Therefore, the graph of the solution to the inequality -1/5m > -2 is an open circle to the left of 10 on a number line, and any value of 'm' less than 10 satisfies the inequality.
To solve the inequality -1/5m > -2, we need to isolate the variable "m" on one side of the inequality sign.
Step 1: Multiply both sides of the inequality by -5 (to remove the fraction):
(-1/5m)(-5) > (-2)(-5)
m < 10
Step 2: Now let's graph the solution. Draw a number line and mark the point where m is equal to 10 with an open circle (since it is not included in the solution).
-∞ 10
------------------------
────○───>
Step 3: As the inequality is m < 10, shade the part of the number line that is to the left of 10 since all values less than 10 satisfy the inequality.
-∞ 10
------------------------
<────○───>
Step 4: Finally, let's check the solution by substituting a value from the shaded region into the original inequality. Let's choose m = 9:
-1/5(9) > -2
-9/5 > -2
Since -9/5 is indeed greater than -2, the shaded region represents the correct solution.
Therefore, the solution to the inequality -1/5m > -2 is m < 10, and it can be represented graphically as m being any value to the left of 10 on the number line.