Question

Select all the values of x that make the equation |3x + 4| − 9 = 0 true. A. 1 23 B. −1 23 C. 4 13 D. −4 13 E. 5 23 F. −5 23

Answer 1

To find the values of x that make the equation |3x + 4| - 9 = 0 true, we can solve for x by considering two cases: when (3x + 4) is positive and when it is negative. The solutions are x = 5/3 and x = -13/3.

Step-by-step explanation:

To find the values of x that make the equation |3x + 4| - 9 = 0 true, we need to solve for x.

First, we can add 9 to both sides of the equation to eliminate the constant term: |3x + 4| = 9.

Now we can solve for two cases: when (3x + 4) is positive and when it is negative.

Case 1: (3x + 4) is positive:

3x + 4 = 9. Subtracting 4 from both sides, we get 3x = 5. Dividing both sides by 3, we find x = 5/3.

Case 2: (3x + 4) is negative:

-(3x + 4) = 9. Distributing the negative sign, we have -3x - 4 = 9. Adding 4 to both sides, we get -3x = 13. Dividing both sides by -3, we find x = -13/3.

So, the values of x that make the equation true are x = 5/3 and x = -13/3.