Question

Решить уравнение:|2x-3|=2

Answer 1

$|2x - 3| = 2$

Возможны 2 случая открытия модуля:

1. При 2х-3>0; х>1.5

Модуль открываем со знаком плюс:

$2x - 3 = 2 \\ 2x = 5 \\ x = 2.5$

2. При 2х-3<0; х<1.5

Модуль открываем со знаком минус:

$- (2x - 3) = 2 \\ 2x - 3 = - 2 \\ 2x = 1 \\ x = 0.5$

Ответ: 0.5, 2.5

Answer 2

если модуль то уравнение имеет два значения

первое :

$2x - 3 = 2 \\ 2x = 2 + 3 \\ 2x = 5 \\ x = \frac{5}{2} \\ x = 2 \times \frac{1}{2}$

второе :

$2x - 3 = - 2 \\ 2x = - 2 + 3 \\ 2x = 1 \\ x = \frac{1}{2}$

Answer 3

To solve the absolute value equation |2x - 3| = 2, we need to consider two cases since the absolute value can result in two different values based on the expression inside it:

Case 1: (2x - 3) = 2 Case 2: -(2x - 3) = 2

Let's solve each case separately:

Case 1: (2x - 3) = 2

Add 3 to both sides: 2x = 2 + 3 2x = 5

Divide both sides by 2: x = 5/2

Case 2: -(2x - 3) = 2

Distribute the negative sign: -2x + 3 = 2

Subtract 3 from both sides: -2x = 2 - 3 -2x = -1

Divide both sides by -2: x = -1 / -2 x = 1/2

So the solutions to the equation |2x - 3| = 2 are x = 5/2 and x = 1/2.