Solve the inequality. Graph and check your solution.
-3h <= 15
Which is the correct graph?
The correct graph is:
-3h <= 15
We can solve the inequality by dividing both sides by -3, remembering to reverse the inequality sign when dividing by a negative number:
h >= -5
The solution is h is greater than or equal to -5. The graph would be a number line with a filled-in circle at -5 and an arrow extending to the right.
To solve the inequality -3h <= 15, we need to isolate the variable h.
First, we divide both sides of the inequality by -3. However, since we are dividing by a negative number, we need to flip the direction of the inequality.
-3h <= 15
h >= 15 / -3
h >= -5
Now we have h greater than or equal to -5. This means that any value of h that is greater than or equal to -5 will make the inequality true.
To graph this inequality, we can create an open circle at -5 on the number line to represent h = -5 (since it is not included in the solution). Then, we shade the region to the right of -5 to represent all the values greater than -5.
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-5
In the graph, the open circle indicates that -5 is not included in the solution, and the shaded region to the right of -5 represents all the values greater than -5.
To check the solution, you can pick any value greater than -5 and substitute it into the inequality. If the inequality is true, the solution is correct. For example, if we choose h = 0, we can substitute it into the inequality:
-3h <= 15
-3(0) <= 15
0 <= 15
Since 0 is less than or equal to 15, the inequality is true for h = 0. We can repeat this process for other values in the shaded region to further verify the solution.
To solve the inequality -3h <= 15, you can begin by dividing both sides of the inequality by -3. However, when dividing by a negative number, you need to flip the inequality sign to maintain the inequality's direction.
So, dividing both sides by -3 gives: h >= -5.
To graph the solution h >= -5 on a number line, you can represent all the values equal to or greater than -5. Since there is no restriction on any values larger than -5, you would draw a closed dot at -5, and draw a solid line extending to the right.
The correct graph would show a closed dot at -5 on the number line and a solid line extending to the right. All values greater than or equal to -5 would be shaded in.
You can check your solution by substituting a value into the inequality. For example, if we substitute h = -5, we get: -3(-5) = 15, which is true. This confirms that the solution is correct.