Choose the correct solution and graph for the inequality. x - 8 <= - 14
The correct solution for the inequality x - 8 <= -14 is x <= -6.
To graph this solution, we can represent all the values of x less than or equal to -6 on a number line. We can mark -6 with a closed circle and shade the line to the left of -6 to represent all the values that make the inequality true.
Here is the graph:
To solve the inequality x - 8 <= -14, we will isolate the variable x step-by-step.
Step 1: Add 8 to both sides of the inequality:
x - 8 + 8 <= -14 + 8
x <= -6
The solution to the inequality is x <= -6.
To graph the solution on a number line, we represent all values of x that are less than or equal to -6. We can draw an open circle at -6, indicating that the value of x can be equal to -6, and shade the region to the left of -6 to represent all values less than -6.
Here is a visual representation of the solution on a number line:
-∞========================•------------------------>
-6
To solve the inequality x - 8 <= -14, we need to isolate the variable x.
First, add 8 to both sides of the inequality to get rid of the constant term:
x - 8 + 8 <= -14 + 8
x <= -6
So the solution to the inequality is x <= -6.
Now let's graph the solution on a number line.
Start by plotting a point at -6, and then draw a closed circle at that point to show that -6 is included in the solution.
Finally, draw a line arrow pointing to the left to indicate that all the numbers less than or equal to -6 are part of the solution.
Here's how the graph would look:
-∞ -6 ∞
─┈┈┈·───►┈┈┈┈┈┈┈┈┈┈┈┈┈┈
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