Solve the inequality. Graph and check your solutions.
-4/5<r-4/5
To solve the inequality, we will first add 4/5 to both sides:
-4/5 < r - 4/5 + 4/5
This simplifies to:
-4/5 < r
We can also write this inequality as:
r > -4/5
To graph this inequality, we will use an open circle at -4/5 on the number line to show that -4/5 is not included in the solution. Then, we will shade the region to the right of -4/5 to represent all values that are greater than -4/5.
Checking the solutions, any value of r that is greater than -4/5 will satisfy the inequality. For example, if we plug in r = 0, we get:
-4/5 < 0 - 4/5
-4/5 < -4/5
This is true, so the solution is correct.
To solve the inequality, we will first simplify the expression:
-4/5 < r - 4/5
Adding 4/5 to both sides of the inequality, we get:
-4/5 + 4/5 < r - 4/5 + 4/5
Simplifying:
0 < r
Graphically, this means that all values to the right of 0 on the number line are solutions. Since there are infinite numbers greater than 0, the graph would be an open circle at 0 with an arrow pointing to the right.
To check the solutions, we can substitute some values greater than 0 into the inequality and see if they hold true. For example, if we substitute r = 1, the inequality becomes:
-4/5 < 1 - 4/5
Simplifying:
-4/5 < 1/5
This is true, so r = 1 is a valid solution.
Similarly, if we substitute r = -1 into the inequality, we get:
-4/5 < -1 - 4/5
Simplifying:
-4/5 < -9/5
This is false, so r = -1 is not a valid solution.
Therefore, the solutions to the inequality are all real numbers greater than 0.
To solve the inequality \(\frac{-4}{5}<r-\frac{4}{5}\), we can follow these steps:
Step 1: Add \(\frac{4}{5}\) to both sides of the inequality. This step will help isolate the variable \(r\).
\(\frac{-4}{5}+\frac{4}{5}<r-\frac{4}{5}+\frac{4}{5}\)
Simplifying the left side, we get:
\(0<r-\frac{4}{5}\)
Step 2: Simplify the right side by adding \(\frac{4}{5}\) and \(r\).
\(0<r-\frac{4}{5}+\frac{4}{5}\)
Simplifying further:
\(0<r\)
The solution to the inequality \(\frac{-4}{5}<r-\frac{4}{5}\) is \(r>0\).
To graph the solution, we can plot all the values of \(r\) that are greater than zero on a number line. We use an open circle to indicate that zero itself is not included in the solution.
--------o----------------->
Here, the open circle represents zero, and the arrow pointing to the right indicates all the values greater than zero that satisfy the inequality.
To check whether the solution is correct, substitute any value greater than zero into the original inequality and see if the inequality holds.
For example, if we substitute \(r=1\) into the original inequality:
\(\frac{-4}{5}<1-\frac{4}{5}\)
Simplifying both sides, we get:
\(\frac{-4}{5}<\frac{1}{5}\)
Since \(\frac{-4}{5}\) is indeed less than \(\frac{1}{5}\), the inequality holds true.
You can perform similar checks for other values greater than zero, and you will find that the inequality holds for all such values.