Solve the equation. Graph and check your solutions. |x| + 9 = 11 Solve the equation for x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. There is no solution.
|x| + 9 = 11
Subtract 9 from both sides:
|x| = 2
For x to be equal to 2, the absolute value of x should be equal to 2 or -2.
So, x = 2 or x = -2.
The solution to the equation is x = 2, -2.
(OA) x = 2, -2
To solve the equation |x| + 9 = 11, we need to isolate the absolute value expression on one side of the equation. Here's the step-by-step process:
1. Subtract 9 from both sides of the equation:
|x| = 11 - 9
|x| = 2
2. Once |x| is isolated, we can rewrite the equation as two separate equations, one with a positive value and the other with a negative value:
x = 2 or x = -2
Now, let's graph and check the solutions.
To graph the equation, plot the two solutions on a number line:
-3 -2 -1 0 1 2 3
------------------------------------
| |
-2 2
The two solutions are x = 2 and x = -2.
To check the solutions, substitute them back into the original equation:
For x = 2:
|2| + 9 = 11
2 + 9 = 11
11 = 11 (True)
For x = -2:
|-2| + 9 = 11
2 + 9 = 11
11 = 11 (True)
Both solutions satisfy the original equation, so the correct choice is:
OA. x = 2, -2
To solve the equation |x| + 9 = 11, we need to isolate the variable x. Here's how we can do that:
1. Start by subtracting 9 from both sides of the equation:
|x| + 9 - 9 = 11 - 9
This simplifies to: |x| = 2.
2. Now, we have an absolute value equation. Recall that the absolute value of a number is its distance from 0 on the number line. So, the equation |x| = 2 represents two possible solutions: x = 2 and x = -2.
3. To graph and check the solutions, we'll plot these two points on the number line and substitute them back into the original equation to verify if they satisfy it.
Plotting x = 2: We consider the positive value of 2, so we place a point on the number line at position 2.
|2| + 9 = 11
2 + 9 = 11
11 = 11 (satisfied)
Plotting x = -2: We consider the negative value of 2, so we place a point on the number line at position -2.
|-2| + 9 = 11
2 + 9 = 11
11 = 11 (satisfied)
Both solutions, x = 2 and x = -2, satisfy the given equation. Therefore, the correct choice is:
OA. x = 2, -2