Solve the equation?

Question

The equation may have 0, 1, or 2 solutions. If there is no solution, enter none, if there is one solution, type that number (as a fraction if necessary) ; if there are two solution, enter them separated with a comma.

l 2n - 3 l = 7

Answer 1

You have to consider a positive & negative solution for this.

2n - 3 = 7
2n = 10
n = 5

- (2n - 3) = 7
-2n + 3 = 7
-2n = 4
n = -2

n = -2, 5

Answer 2

So 2n - 3 = 7 OR 2n - 3 = -7
→ 2n = 10 OR 2n = -4
→ x = 5 OR n = -2.

The solutions are 5, -2.

Answer 3

When you do absolute equations, you will get two solutions for this:

| 2n-3 |=7
2n-3=7
2n=10
n=5

| 2n-3 |=-7
2n-3=-7
2n=-4
n=-2

The solutions are -2 and 5.

Check:
| 2(5)-3 |=7
10-3=7
7=7

| 2(-2)-3 |=7
| -4-3 |=7
| -7 |=7
7=7

Answer 4

|2n - 3| = 7 means that:-
2n - 3 = 7 and 2n - 3 = - 7
n = 5 , n = - 2

Answer 5

2n - 3 = 7
and
2n - 3 = -7

there you go....

n = 5, -2

Answer 6

l 2n-3l = 7
2n - 3 = 7 or 2n - 3 = -7
2n = 10 or 2n = -4
n = 5 or n = -2

So, n= -2, 5

Answer 7

because it is an absolute value, you have to solve this problem two times....once for a positive answer and once for a negative answer (which would be cancled out by the absolute value signes.)

In short there are two answers : 5, -2