Question

Solve the equation. Graph and check your solutions.
lxl+9=12

Answer 1

To solve the equation |x| + 9 = 12, we must first isolate the absolute value by subtracting 9 from both sides.

| x | + 9 - 9 = 12 - 9
| x | = 3

Since the absolute value of a number is always non-negative, we can rewrite the equation as two separate cases.

Case 1: x = 3
In this case, the absolute value of x is already 3, so the equation is true. Therefore, x = 3 is one solution.

Case 2: x = -3
In this case, the absolute value of x is |-3| = 3. Therefore, x = -3 is another solution.

To graph these solutions, we plot the points (3, 0) and (-3, 0) on the number line.

Checking the solutions:
For x = 3: |3| + 9 = 12, which is true.
For x = -3: |-3| + 9 = 12, which is also true.

Therefore, the solutions to the equation |x| + 9 = 12 are x = 3 and x = -3.

The graph of the equation would be a number line with a filled circle at 3 and -3, representing the solutions.