Question

/х/+/х-6/=6 /- модуль

Answer 1

Возможны два решения:
1) х+x-6=6
2x=6+6
2x=12|:2
x=6
2) -x-x+6=6
-2x=6-6
-2x=0|:(-2)
x=0

Answer 2

To solve the equation |x| + |x-6| = 6, we need to consider the different cases based on the sign of the expressions inside the absolute value bars.

Case 1: (x ≥ 0) and (x-6 ≥ 0) In this case, both x and (x-6) are non-negative, so the absolute value signs are not needed. So, the equation becomes: x + (x-6) = 6

Solving for x: 2x - 6 = 6 2x = 12 x = 6

Case 2: (x ≥ 0) and (x-6 < 0) In this case, x is non-negative, but (x-6) is negative, so we need to take the negative value inside the absolute value bars. So, the equation becomes: x - (x-6) = 6

Solving for x: x - x + 6 = 6 6 = 6

The above equation is true for any value of x since both sides are equal, but it doesn't provide any specific solutions.

Case 3: (x < 0) and (x-6 ≥ 0) In this case, x is negative, but (x-6) is non-negative, so we need to take the positive value inside the absolute value bars. So, the equation becomes: -x + (x-6) = 6

Solving for x: -x + x - 6 = 6 -6 = 6

The above equation is not true for any value of x, so there are no solutions in this case.

Case 4: (x < 0) and (x-6 < 0) In this case, both x and (x-6) are negative, so we need to take the negative values inside both absolute value bars. So, the equation becomes: -x - (x-6) = 6

Solving for x: -x - x + 6 = 6 -2x + 6 = 6 -2x = 0 x = 0

Now, we have two potential solutions: x = 6 (from Case 1) and x = 0 (from Case 4).

However, upon checking, x = 6 is not a valid solution because it makes one of the absolute value terms negative in the original equation: |6| + |6 - 6| = 6 6 + |0| = 6 6 + 0 = 6 6 = 6

But, x = 0 is indeed a valid solution: |0| + |0 - 6| = 6 0 + |(-6)| = 6 0 + 6 = 6 6 = 6

So, the only valid solution to the equation |x| + |x-6| = 6 is x = 0.