Solve and graph the equation. |x| = 4 Select the correct choice and, if necessary, fill in the answer box in your choice below.
A. x = (Simplify your answer. Use a comma to separate answers as needed.)
B. There is no solution.
A. x = 4 or x = -4
To solve the equation |x| = 4, we need to consider two cases:
1. When x is positive or zero: In this case, |x| is equal to x. So the equation becomes x = 4.
2. When x is negative: In this case, |x| is equal to -x. So the equation becomes -x = 4.
Now we solve each case separately:
Case 1: x = 4
Simplifying, we get x = 4.
Case 2: -x = 4
To solve for x, we multiply both sides of the equation by -1:
-x * -1 = 4 * -1
This gives us x = -4.
So there are two solutions to the equation: x = 4 and x = -4.
To graph these solutions, we plot the points (4, 0) and (-4, 0) on the number line.
To solve the equation |x| = 4, we need to consider two cases: when x is positive and when x is negative.
Case 1: When x is positive, the equation |x| = 4 becomes x = 4.
Case 2: When x is negative, the equation |x| = 4 becomes -x = 4. Solving for x, we get x = -4.
So the solutions to the equation |x| = 4 are x = 4 and x = -4.
To graph the equation, we plot these two values on a number line:
-4 0 4
|---|---|---|---|---|---|---|
x
The graph consists of two points: -4 and 4, both marked with an open circle (since absolute value equations do not include the endpoints). The line between -4 and 4 is also included because all values between -4 and 4 satisfy the equation.