Which graph shows the solution to the inequality?
x - 4 ≥ -1
graph A is a number line with -10 through 3
graph b is a number line with 3 through 10 with a circle on 3
graph c is a number line with 5 through 10
graph d is a number line with 3 through 10
X-4>-1
To solve the inequality x - 4 ≥ -1, you can follow these steps:
1. Add 4 to both sides of the inequality to isolate "x":
x - 4 + 4 ≥ -1 + 4
Simplifying, we get: x ≥ 3
2. Now, we need to represent the solution on a number line.
Looking at the given options, graph B is the correct one. It is a number line with 3 through 10, and there is a closed circle on 3.
This represents that x is equal to or greater than 3, as required by the inequality.
To determine which graph shows the solution to the given inequality x - 4 ≥ -1, we need to understand the meaning of this inequality and then analyze each graph.
The given inequality x - 4 ≥ -1 represents a statement that states that the value of "x" minus 4 is greater than or equal to -1.
To solve this inequality, we can start by isolating the variable "x" by adding 4 to both sides of the inequality:
x - 4 + 4 ≥ -1 + 4
This simplifies to:
x ≥ 3
Now that we have the solution, we can evaluate the graphs:
Graph A: The number line ranges from -10 through 3. The inequality x ≥ 3 is not satisfied since it includes the equal sign, indicating "greater than or equal to," and the number 3 is not included in this graph.
Graph B: The number line ranges from 3 through 10 with a closed circle on 3. Since the inequality states x ≥ 3, this graph matches the solution. The closed circle indicates that 3 is included in the solution.
Graph C: The number line ranges from 5 through 10. As the inequality states x ≥ 3, this graph does not contain the entire range of the solution.
Graph D: The number line ranges from 3 through 10. This graph matches the solution, representing x ≥ 3, including the number 3.
Based on this analysis, the graph that shows the solution to the inequality x - 4 ≥ -1 is Graph D, which ranges from 3 through 10.
x - 4 ≥ -1
x ≥ 3
So your graph should show a number line, with a solid "dot" on the 3
and the arrow going to the right.
Where does the 10 come from? Does you line stop at 10?