Question

Determine all of the values of x for which | -3 - x | = 5. Explain your reasoning. Kassidy charges a flat rate for mowing yards in her neighborhood, shown on the graph below.

Answer 1

The values of x that satisfy the equation | -3 - x | = 5 are x = -8 and x = 2, since the absolute value represents a distance on the number line which can be achieved in two ways, by having the quantity inside be either positive or negative.

Step-by-step explanation:

To determine all of the values of x for which | -3 - x | = 5, we have to consider the definition of absolute value which states that it is the distance of a number on the number line from zero, regardless of direction. This means we have two scenarios to consider, one where -3 - x is positive and one where it is negative. Let's solve both equations:

• When -3 - x is positive, we have -3 - x = 5. Solving for x gives us x = -8.
• When -3 - x is negative, we consider -(-3 - x) = 5 which simplifies to 3 + x = 5. Solving for x gives us x = 2.

Therefore, the two values of x that satisfy the equation | -3 - x | = 5 are x = -8 and x = 2.