Question

|x|=7

Solve the following absolute value equation
What is the solution to the absolute value equation |x| = 7?

A) x = 7
B) x = -7
C) x = 7 or x = -7
D) No solution

Answer 1

The solution to the absolute value equation |x| = 7 is C) x = 7 or x = -7, because absolute value represents the distance from zero, which can be either positive or negative.

Step-by-step explanation:

To solve the absolute value equation |x| = 7, you need to consider the definition of absolute value. The absolute value of a number is the distance of the number from zero on the number line, regardless of direction. Therefore, when you have an equation of the form |x| = a, where a is a positive number, there are two possible solutions for x: one positive and one negative, as both would be at the same distance from zero.

Solving |x| = 7 means finding the number x that is 7 units away from zero. There are two numbers that satisfy this condition: 7 and -7.

Thus, the equation |x| = 7 has two solutions:

• x = 7
• x = -7

The correct answer to the given question is therefore C) x = 7 or x = -7.