Question

The table below shows two equations:
Equation 1 |4x − 3|− 5 = 4
Equation 2 |2x + 3| + 8 = 3
Which statement is true about the solution to the two equations?
* Equation 1 and equation 2 have no solutions.
* Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
* The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution. *
* The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.

Answer 1

Answer:

Option C is correct.

Step-by-step explanation:

Equation 1 |4x − 3|− 5 = 4

Adding +5 on both sides

|4x − 3|− 5 +5 = 4 +5

|4x − 3| = 9

Apply absolute rule:

IuI = a and a>0 then u = a and u = -a

so, 4x-3 = 9 and 4x-3 = -9

Solving

4x = 9+3   and 4x = -9+3

4x = 12      and 4x = -6

x = 12/4     and x = -6/4

x = 3          and x = -3/2 or -1.5

Equation 2 |2x + 3| + 8 = 3

Adding -8 on both sides

|2x + 3| + 8 -8 = 3 -8

|2x + 3|  = -5

Apply absolute rule:

IuI = a and a>0 then u = a and u = -a

But we cannot apply absolute rule because in our case a < 0 i.e -5

So, Equation 2 has no solutions.

Hence Option C The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution is correct.