Question

|х|+6=1|х+5|=1 сколько будет х? желательно написать подробно даю 20 балов ​

Answer 1

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Answer 2

Solving the Equation Step by Step

To solve the equation |x| + 6 = |x + 5| = 1 and find the value of x, we can break it down into different cases based on the absolute value expressions.

1. Case 1: x ≥ -5 - When x ≥ -5, the equation |x + 5| simplifies to x + 5. - So, the original equation becomes |x| + 6 = x + 5 = 1.

Now, let's solve for x in this case.

Subtracting 5 from both sides of the equation gives us: |x| + 6 - 5 = x + 5 - 5 which simplifies to: |x| + 1 = x

Now, we have two sub-cases to consider: - Sub-case 1.1: x ≥ 0 - When x ≥ 0, the equation |x| simplifies to x. - So, the equation becomes x + 1 = x, which simplifies to 1 = 0. - This sub-case does not yield a valid solution.

- Sub-case 1.2: x < 0 - When x < 0, the equation |x| simplifies to -x. - So, the equation becomes -x + 1 = x, which simplifies to 1 = 2x. - Solving for x in this sub-case, we get x = 1/2.

2. Case 2: x < -5 - When x < -5, the equation |x + 5| simplifies to -(x + 5). - So, the original equation becomes |x| + 6 = -(x + 5) = 1.

Now, let's solve for x in this case.

Subtracting 6 from both sides of the equation gives us: |x| + 6 - 6 = -(x + 5) - 6 which simplifies to: |x| = -(x + 11)

We can't solve for x in this case as it leads to a contradiction.

Conclusion

The equation |x| + 6 = |x + 5| = 1 has one solution: x = 1/2. This solution is obtained from the first case where x < 0.

So, the value of x that satisfies the given equation is x = 1/2.