Question

(02.03 LC)

How many solutions does the following equation have? (5 points)

|4x + 12| = 0


No solution

One solution

Two solutions

Infinitely many solutions

Answer 1

One solution

Explanation:

Based on a property of a Modular Function. If |x| =0 then x=0

|4x +12|=0

4x+12=0

4x+12-12=-12

4x=-12 *1/4

x=-3 S={-3}

Check the graph below to see the point (-3,0) i.e. x=-3 as the only solution that satisfy the equation

Answer 2

One solution

_____

An absolute value is zero only when its argument is zero. The linear expression that is the argument will be zero for only one value of x: -3.