Solve the inequality. Graph and check your solutions.
- 3/4 >= r - 3/4
To solve the inequality -3/4 >= r - 3/4, we need to isolate the variable r on one side of the inequality sign. Here's how you can do it:
Step 1: Add 3/4 to both sides of the inequality to eliminate the -3/4 term:
-3/4 + 3/4 >= r - 3/4 + 3/4
Simplifying, we get:
0 >= r
Step 2: Since 0 is greater than or equal to any value of r, this inequality is true for all real numbers. In other words, r can be any real number.
To graph the solution, you can draw a number line and mark the point 0. From there, include all real numbers to the right of 0 on the number line. This represents the solution to the inequality 0 >= r.
To check the solution, you can substitute any value for r in the original inequality and see if it holds true. Since the inequality is true for all real numbers, any value you substitute will yield a true statement.
To solve the inequality -3/4 ≥ r - 3/4, we can follow these steps:
Step 1: Add 3/4 to both sides of the inequality:
-3/4 + 3/4 ≥ r - 3/4 + 3/4
0 ≥ r
Step 2: Graph the inequality:
To graph the inequality 0 ≥ r, we need to draw a number line and shade the region to the right of or on the point 0. Since 0 is included in the solution set, we use a solid dot at 0.
-∞-------●============>
0
Step 3: Check the solution:
We can choose any value on the line, and if the inequality holds true, it is a valid solution.
Let's choose a value less than or equal to 0, for example, -1.
Substitute -1 into the original inequality: -3/4 ≥ -1 - 3/4.
-3/4 ≥ -7/4.
Since -3/4 is greater than -7/4, the inequality holds true.
Therefore, the solution to the inequality is r ≤ 0.
To solve the inequality, we will first add 3/4 to both sides:
- 3/4 + 3/4 >= r - 3/4 + 3/4
Simplifying both sides:
0 >= r
The solution to the inequality is any value of r that is less than or equal to 0.
To graph the solution, we will plot all values of r that are less than or equal to 0 on a number line. We will use a closed circle to represent the value 0, since it is included in the solution. Then we will shade to the left of the circle to represent all values less than 0.
The graph will look like this:
<-------o==============================================>
Now, let's check some values to see if they satisfy the inequality.
- If we choose r = 0, the inequality becomes: -3/4 >= 0 - 3/4
Simplifying both sides, we get: -3/4 >= -3/4
This is true, so r = 0 satisfies the inequality.
- If we choose r = -1, the inequality becomes: -3/4 >= -1 - 3/4
Simplifying both sides, we get: -3/4 >= -7/4
This is also true, so r = -1 satisfies the inequality.
- If we choose r = 1, the inequality becomes: -3/4 >= 1 - 3/4
Simplifying both sides, we get: -3/4 >= 1/4
This is not true, so r = 1 does not satisfy the inequality.
Therefore, the solutions to the inequality are r ≤ 0.