solve the inequality. Graph the solution set.
5r + 4 is less than or equal to 5
5r+4 <= 5
5r <= 1
r <= 1/5
I assume you can graph that on the number line.
Yeah. Thank you!
To solve the inequality 5r + 4 ≤ 5, we can start by isolating the variable r.
Step 1: Subtract 4 from both sides of the inequality:
5r + 4 - 4 ≤ 5 - 4
5r ≤ 1
Step 2: Divide both sides of the inequality by 5:
(5r)/5 ≤ 1/5
r ≤ 1/5
The solution set for this inequality is all real numbers less than or equal to 1/5. We can represent this solution set on a number line as follows:
<----------------------[0]-----------[1/5]--------------------------------->
To graph the solution, we represent the number line starting from zero and mark the point 1/5. The shaded region to the left of or on the point 1/5 represents the solution set.
Solution set: (-∞, 1/5]
To solve the inequality 5r + 4 ≤ 5, we need to first isolate the variable r on one side of the inequality sign.
1. Subtract 4 from both sides of the inequality:
5r + 4 - 4 ≤ 5 - 4
This simplifies to: 5r ≤ 1
2. Divide both sides of the inequality by 5:
(5r)/5 ≤ 1/5
This simplifies to: r ≤ 1/5
The solution set for this inequality is r ≤ 1/5. In terms of graphing, we can represent the solution set on a number line:
On a number line, we mark a point at 1/5, and draw a closed circle at that point to indicate that it is included in the solution set. Then, we shade the region to the left of the point, as numbers less than or equal to 1/5 are within the solution set.
Here is a visual representation of the solution set on a number line:
------------------------------------●
r ≤ 1/5
The graph shows that all values to the left of and including 1/5 are solutions to the given inequality.