Question

-|x|=-7 ; |-n|=6 хелп

Answer 1

-|x|=-7
|x|=7

|n|=6
n=6

Answer 2

To solve the equation |-n| = 6, we need to consider two cases for the absolute value of n.

Case 1: n is positive or zero (n ≥ 0). In this case, |-n| = n, so we can rewrite the equation as: n = 6

Case 2: n is negative (n < 0). In this case, |-n| = -n, so we can rewrite the equation as: -n = 6

Now, let's solve each case separately:

Case 1: n = 6 Since n is positive or zero, the solution is n = 6.

Case 2: -n = 6 To solve for n, we need to isolate it on one side of the equation. To do that, we can multiply both sides by -1: (-1) * (-n) = (-1) * 6 n = -6

So, in this case, the solution is n = -6.

Now, let's move on to the equation -|x| = -7.

To solve this equation, we'll follow a similar approach, considering two cases for the absolute value of x.

Case 1: x is positive or zero (x ≥ 0). In this case, -|x| = -x, so we can rewrite the equation as: -x = -7

Now, solve for x by multiplying both sides by -1: (-1) * (-x) = (-1) * (-7) x = 7

Case 2: x is negative (x < 0). In this case, -|x| = x, so we can rewrite the equation as: x = -7

Now we have two potential solutions:

Case 1: x = 7 Case 2: x = -7

So, the solutions to the equation -|x| = -7 are x = 7 and x = -7.