Question

Розв'яжіть рівняння1)|х|=18 2) 11-|х|=11​

Answer 1

Правило.

|a| = a, если a > 0; (положительное)

|a| = 0, если a = 0;

|a| = -a, если a < 0 (отрицательное)

Решение.

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  $\bf x_2 = -18$

  • $\bf 11- |x| = 11$

  $\bf -|x| = 11 - 11$

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  $\bf x = 0$

  Ответ: 1) x₁ = 18, x₂ = -18; 2) x = 0.

Answer 2

1. |x| = 18: To solve this equation, we have two cases:

Case 1: x = 18

Case 2: x = -18

So, the solutions to the equation |x| = 18 are x = 18 and x = -18.

2. 11 - |x| = 11: To solve this equation, we can simplify it as follows:

11 - |x| = 11

Now, subtract 11 from both sides:

-|x| = 0

To remove the negative sign, we can take the absolute value of both sides:

|x| = 0

The absolute value of any number is always non-negative, and it is 0 only when the number itself is 0. Therefore, the solution to the equation is:

x = 0