Solve the inequality. Graph and check your solutions.
- 3/4 >= r - 3/4
Choose the correct graph below.
The inequality is: - 3/4 ≥ r - 3/4
To solve for r, we add 3/4 to both sides:
- 3/4 + 3/4 ≥ r - 3/4 + 3/4
0 ≥ r
So the solution for r is r ≤ 0.
Graph:
On a number line, mark a solid dot at 0 and shade the part to the left of 0.
Thus, the correct graph is:
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r ≤ 0
To solve the inequality -3/4 >= r - 3/4, we need to isolate the variable r.
First, let's simplify the equation:
-3/4 >= r - 3/4
Combine like terms on the right side:
-3/4 + 3/4 >= r - 3/4 + 3/4
0 >= r
Now we have the simplified inequality 0 >= r.
To graph and check the solutions, we can plot the points on a number line.
Draw a number line and mark a point at 0. Since the inequality includes the equal sign (0 >= r), we'll fill in the point at 0 with a solid dot to represent that it is included in the solution set.
Since all values less than or equal to 0 are solutions, shade the line to the left of 0 to represent the solution set.
Now, let's check the solutions:
Choose any value less than or equal to 0, let's say -1.
Substitute -1 into the original inequality:
-3/4 >= -1 - 3/4
Simplify:
-3/4 >= -7/4
Since -3/4 is greater than or equal to -7/4, the inequality holds true for this value.
Based on this, we can conclude that all values less than or equal to 0 are solutions to the inequality -3/4 >= r - 3/4.
Therefore, the correct graph would show a filled-in dot at 0 on the number line and a shaded line to the left representing all values less than or equal to 0.
To solve the inequality -3/4 >= r - 3/4, we can first add 3/4 to both sides to isolate r.
-3/4 + 3/4 >= r - 3/4 + 3/4
0 >= r
This means that any value of r that is less than or equal to zero satisfies the inequality.
To graph the solution, we can draw a number line and mark zero with an open circle (since the inequality is not inclusive of zero). Then, shade the left-hand side of the number line to represent all values of r that satisfy the inequality.
The correct graph would be the number line with an open circle at zero (0) and a shaded line to the left of zero.