Question

1) | x-2 |=12 2) | x-5 |=18

Answer 1

Уравнение | x-2 |=12 можно решить, разделив его на две отдельные случая: x-2=12 и x-2=-12.
Если x-2=12, то x=14.

Если x-2=-12, то x=-10.

Таким образом, решения уравнения x=14 и x=-10.

Уравнение | x-5 |=18 можно решить, разделив его на две отдельные случая: x-5=18 и x-5=-18.
Если x-5=18, то x=23.

Если x-5=-18, то x=-13.

Таким образом, решения уравнения x=23 и x=-13

Answer 2

To solve the absolute value equations you provided, we need to consider both the positive and negative cases for the expression within the absolute value. Let's solve each equation separately:

1. |x - 2| = 12:

Positive case: x - 2 = 12 x = 12 + 2 x = 14

Negative case: -(x - 2) = 12 -x + 2 = 12 -x = 12 - 2 -x = 10 x = -10

So the solutions for the equation |x - 2| = 12 are x = 14 and x = -10.

2. |x - 5| = 18:

Positive case: x - 5 = 18 x = 18 + 5 x = 23

Negative case: -(x - 5) = 18 -x + 5 = 18 -x = 18 - 5 -x = 13 x = -13

Therefore, the solutions for the equation |x - 5| = 18 are x = 23 and x = -13.