Question

A)2×|x-3|=10b)14×|3x-7|=-70​

Answer 1

Ответ:

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Answer 2

Ответ:

a) x1 = -2, x2 = 8

b) x∈∅

Пошаговое объяснение:

a) 2|x-3|=10 [Делим обе части на 2]

|x-3|=5 [Раскрываем скобки. Подмодульное выражение равно или пяти, или минус пяти]

x-3 = 5 [Прибавляем 3 к обеим частям обеих уравнений]

x-3 = -5

x1 = 8

x2 = -2

b) 14|3x-7|=-70​ [Делим обе части на 14]

|3x-7|=-5 [Модуль не может быть меньше нуля. Поэтому уравнение решений не имеет.]

x∈∅

Answer 3

Let's solve these absolute value equations step by step:

A) 2|x - 3| = 10

To solve this equation, you can start by isolating the absolute value term. Divide both sides of the equation by 2:

|x - 3| = 5

Now, you have two cases to consider: when the expression inside the absolute value is positive and when it's negative.

Case 1: x - 3 is positive: x - 3 = 5

Now, add 3 to both sides:

x = 5 + 3 x = 8

Case 2: x - 3 is negative: -(x - 3) = 5

Now, distribute the negative sign:

-x + 3 = 5

Subtract 3 from both sides:

-x = 5 - 3 -x = 2

Now, multiply both sides by -1 to isolate x:

x = -2

So, the solutions to the equation 2|x - 3| = 10 are x = 8 and x = -2.

B) 14|3x - 7| = -70

This equation has no real solutions because the absolute value of any real number is always non-negative (greater than or equal to 0), and the right side of the equation (-70) is negative. Therefore, there are no values of x that will satisfy this equation.