Solve and graph the equation.
lxl=11
To solve the equation |x| = 11, we need to consider two cases:
1) x is positive:
If x is positive, then |x| is just x.
So the equation becomes x = 11.
Therefore, x = 11 is the solution when x is positive.
2) x is negative:
If x is negative, then |x| is -x.
So the equation becomes -x = 11.
Therefore, x = -11 is the solution when x is negative.
Hence, the equation |x| = 11 has two solutions: x = 11 and x = -11.
To graph this equation, we plot these two points on the number line:
-11 ------------ 0 ------------ 11
So the graph would have a filled-in circle at -11 and another filled-in circle at 11, representing the two solutions.
To solve and graph the equation lxl = 11, we first need to understand what the equation represents. The notation |x| refers to the absolute value of x, which means the distance of x from zero on a number line.
In this equation, we want to find all values of x that have an absolute value of 11. To do that, we can set up two separate equations:
1) x = 11
2) x = -11
These equations represent the positive and negative distances of x from zero, which is 11 units in either direction.
Now, let's graph these two equations on a number line. We'll mark the numbers -11 and 11 on the line, and these points will represent the solutions for x.
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
x ------------------ ● ------------------ x
The two dots, one on the left at -11 and the other on the right at 11, represent the solutions of the equation lxl = 11.
To solve the equation |x| = 11, we need to split it into two cases: x is positive, and x is negative.
Case 1: x is positive:
If x is positive, then |x| = x. So we have the equation x = 11.
Case 2: x is negative:
If x is negative, then |x| = -x. So we have the equation -x = 11. To solve for x, we multiply both sides by -1:
-x * -1 = 11 * -1, which simplifies to x = -11.
Therefore, the solutions to the equation |x| = 11 are x = 11 and x = -11.
Now, let's graph the equation y = |x| = 11.
To do this, we need to plot the points (11, 11) and (-11, 11) on a coordinate plane.
The graph will be a V-shaped graph with the vertex at (0, 0) and opening upward.
One leg of the V will pass through (11, 11) and the other leg will pass through (-11, 11).
Here is the graph:
|
|
|
|___(11,11)
|(0,0) (0,0)
|___(-11,11)
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|
|
Keep in mind that the graph of absolute value functions is always a V-shaped graph and its vertex depends on the equation. In this case, the vertex is (0, 0) since there is no constant term attached to the absolute value expression.