Question

9-|x|=9 решение и ответ

Answer 1

9-|x|=9
9-x=9
x=0
9-(-x)=9
9+x=9
x=0
Ответ:x=0

Answer 2

9-|x|=9
-|x|=0
х=0
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Answer 3

To solve the equation |9-|x|| = 9, we need to consider two cases: one where 9-|x| is positive, and the other where it is negative. The absolute value function |y| is defined as follows:

If y ≥ 0, then |y| = y. If y < 0, then |y| = -y.

Case 1: 9-|x| ≥ 0 (i.e., 9-|x| is positive) In this case, we have 9-|x| = 9. Subtract 9 from both sides of the equation: 9 - 9 - |x| = 9 - 9 -|x| = 0

Now, divide both sides by -1 (remember to reverse the inequality sign when dividing by a negative number): -|x| / -1 = 0 / -1 |x| = 0

Case 2: 9-|x| < 0 (i.e., 9-|x| is negative) In this case, we have -(9-|x|) = 9. Multiply both sides by -1 to eliminate the negative sign: 9 - |x| = -9

Now, add |x| to both sides of the equation: 9 - |x| + |x| = -9 + |x| 9 = -9 + |x|

Add 9 to both sides of the equation: 9 + 9 = -9 + 9 + |x| 18 = |x|

Now, we have two separate equations from each case:

1. |x| = 0
2. |x| = 18

Now let's solve each equation individually:

1. |x| = 0: Since the absolute value of any number is non-negative, the only solution for this equation is x = 0.

2. |x| = 18: In this case, there are two possible solutions when x is either positive or negative: a) x = 18 b) x = -18

So the solutions to the original equation are: x = 0, x = 18, and x = -18.