Solve the inequality. Graph and check your solutions.
- 3/4 > r - 3/4
To solve the inequality, we can start by adding 3/4 to both sides to isolate the variable r.
-3/4 + 3/4 > r - 3/4 + 3/4
0 > r
The solution to the inequality is r < 0.
To graph the solution, we can draw a number line and shade everything to the left of 0.
Checking the solution: We can choose a value to the left of 0, such as -1. Plugging it into the inequality:
-3/4 > -1 - 3/4
-3/4 > -7/4
This is true, so the solution is verified.
Graph:
<--------------------0----------------->
<-------------(-∞)-------------------0
Therefore, r < 0 is the solution to the inequality.
To solve the given inequality, we want to isolate the variable on one side of the inequality sign. Let's break down the steps:
Step 1: Simplify the left side of the inequality.
-3/4 is already in simplified form.
Step 2: Combine like terms on the right side of the inequality.
(r - 3/4) can be simplified as (r - 3/4).
Step 3: Simplify the inequality.
-3/4 > r - 3/4
Step 4: Add 3/4 to both sides of the inequality.
-3/4 + 3/4 > r - 3/4 + 3/4 simplifies to 0 > r.
Step 5: Further simplify the inequality.
0 > r
Now let's graph and check the solutions:
To graph this inequality, we will represent it on the number line. We need to first consider what values of r make the inequality true.
Since 0 is greater than any negative number, the solution is all real numbers greater than 0. We represent this on the number line by shading everything to the right of 0, leaving an open circle at 0 to indicate that it is not included in the solution.
-∞ 0========================
Solution: r > 0
To check the solution, substitute a number greater than 0 into the original inequality and verify if it is true.
For example, let's substitute r = 1 into the original inequality:
-3/4 > 1 - 3/4
-3/4 > 1/4
Since -3/4 is indeed greater than 1/4, the solution r > 0 is verified.
Therefore, the solution to the inequality -3/4 > r - 3/4 is r > 0.
To solve the inequality -3/4 > r - 3/4, we can start by adding 3/4 to both sides of the inequality:
-3/4 + 3/4 > r - 3/4 + 3/4
0 > r
So the solution to the inequality is r < 0.
To graph the solution, we can plot all values of r that are less than 0 on a number line. We can represent this by shading the number line to the left of 0:
-----o----------------
...-3 -2 -1 0 1 2...
The open circle at 0 indicates that 0 is not included in the solution. All values to the left of 0 are solutions to the inequality.
To check the solution, we can take any value that is less than 0 and substitute it into the original inequality:
Let's take r = -1:
-3/4 > -1 - 3/4
-3/4 > -7/4
Since -3/4 is greater than -7/4, the inequality holds true for r = -1.
Therefore, the solution to the inequality -3/4 > r - 3/4 is r < 0.