Question

1) |x| +2=172)1x1-2=-123) 2/x|− 6 = 04)/X+21=85) |x-21=06) |x-4|=-5​

Answer 1

Let's solve each of these equations step by step:

1. |x| + 2 = 17

To solve this equation, you can isolate the absolute value expression:

|x| = 17 - 2 |x| = 15

Now, you have two cases to consider, one for each possible value of x:

Case 1: x is positive: x = 15

Case 2: x is negative: -x = 15 x = -15

So, the solutions are x = 15 and x = -15.

2. 1|x| - 2 = -12

Isolate the absolute value expression:

1|x| = -12 + 2 1|x| = -10

Now, just like in the previous problem, consider two cases:

Case 1: x is positive: |x| = -10 (but absolute value can't be negative, so no solution in this case)

Case 2: x is negative: |x| = 10 x = -10

So, the solution is x = -10.

3. 2/|x| - 6 = 0

Isolate the absolute value expression:

2/|x| = 6

Now, divide both sides by 2:

| x | = 3

Again, two cases:

Case 1: x is positive: x = 3

Case 2: x is negative: -x = 3 x = -3

The solutions are x = 3 and x = -3.

4. x + 2 = 8

Isolate x:

x = 8 - 2 x = 6

The solution is x = 6.

5. |x - 21| = 0

This equation has only one solution because the absolute value of any number is always non-negative:

x - 21 = 0

Add 21 to both sides:

x = 21

The solution is x = 21.

6. |x - 4| = -5

This equation has no real solutions because the absolute value of any real number is always non-negative, and it cannot be equal to -5.

So, there are no real solutions to this equation.