Question

|5x-12|=6 12|2x-5|=-20

Answer 1

Ответ:

1) х1 = 3,6; х2 = 1,2

2) Нет решений

Пошаговое объяснение:

1) |5x-12|=6

а) 5x-12=6                                    б) 5x-12=-6  

   5х=18                                            5x=6

    х= 18/5=3,6                                  х=6/5=1,2

2) 12|2x-5|=-20

Нет решений, поскольку левая часть  всегда  положительная или равна 0, а правая  всегда отрицательная.

Answer 2

To solve the absolute value equations:

1. |5x - 12| = 6
2. 12|2x - 5| = -20

We'll start with the first equation:

1. |5x - 12| = 6

First, consider the two cases when the expression inside the absolute value is positive and when it's negative:

Case 1: 5x - 12 is positive: 5x - 12 = 6

Now, solve for x:

5x = 6 + 12 5x = 18 x = 18/5

Case 2: 5x - 12 is negative: -(5x - 12) = 6

Now, solve for x:

-5x + 12 = 6

Subtract 12 from both sides:

-5x = 6 - 12 -5x = -6

Divide by -5 to isolate x:

x = (-6) / (-5) x = 6/5

Now, let's move on to the second equation:

2. 12|2x - 5| = -20

Absolute values are always non-negative, so 12|2x - 5| will be non-negative. Since -20 is negative, there are no real solutions to this equation. In other words, the second equation has no solution in the real number system.

So, the solution to the system of equations is: x = 18/5 and x = 6/5 for the first equation, and no solution for the second equation.