Question

The equation |ax + b| = c must have ?

a. only 1 solution
b. 1 or 2 solutions
c. 0, 1, or 2 solutions
d. 0, 1 or an infinite number of solutions

Answer 1

Answer: Option c

Explanation:

1. By definition |ax + b| = c can be written as:

-ax-b=c if ax+b is greater than zero (ax+b>0)

ax+b=c if ax+b is equal or greater than zero (ax+b
`\geq`0)

This means that this function has two solutions.

2. Then, |ax + b| is always greater than zero. Therefore, if c is less than zero, then the equation has no solution.

3. Therefore, the function can have two solutions if c>0 and no solution is c<0.

Then, the function can have 0,1 or 2 solutions.

Answer 2

0, 1, or 2 solutions

Explanation:

The equation |ax + b| = c

The equation have absolute value symbol

Absolute value always gives us the positive number.

For absolute value function , we need to consider two cases

positive and negative.

|x|=x for positive , and |-x|=x for negative case

For negative case we include negative sign

So |ax + b| = c can be written as 2 equations

(ax+b)=c (ax+b)=-c

So we will get maximum of 2 solutions

The equation |ax + b| = c must have 0, 1, or 2 solutions