Question

|3x-4|=|x=6| |x|-4x=15 реши уравнение

Answer 1

Объяснение:

$|3x - 4| = |x + 6| \\ 3x - 4 = x + 6 \\ 3x - 4 = - (x + 6) \\ x1 = - \frac{1}{2} = - 0.5 \\ x2 = 5$

$|x| - 4x = 15 \\ x - 4x = 15 \: x \geqslant 0 \\ - x - 4x = 15 \: x < 0 \\ x = - 5 \: x \geqslant 0 \\ x = - 3 \: x < 0 \\ x = - 3$

Answer 2

Ответ:

Объяснение:I3x-4I=I x+6I⇔3x-4=x+6 или 3x-4=-(x+6)

                                             2x=10 или  4х=-2

                                             х=5 или  х= -0,5.

2)I xI-4x=15⇔IxI=15+4x⇔{15+4x≥0,x=15+4x или х= - 15-4х ⇔{15+4x≥0,x= -5 или х= - 3 ⇔ х=-3.  (-5 не уд-ет условию 15+4х≥0)                

Answer 3

To solve the given equations, let's break them down one by one:

1. |3x - 4| = |x - 6|

For absolute value equations, we need to consider two cases, one where the expression inside the absolute value is positive, and the other where it's negative.

Case 1: (3x - 4) is positive and (x - 6) is positive. 3x - 4 = x - 6

Solve for x: 3x - x = -6 + 4 2x = -2 x = -2/2 x = -1

Case 2: (3x - 4) is negative and (x - 6) is negative. -(3x - 4) = -(x - 6) -3x + 4 = -x + 6

Solve for x: -3x + x = 6 - 4 -2x = 2 x = 2/(-2) x = -1

Since the values of x in both cases are the same (-1), this is the solution to the equation |3x - 4| = |x - 6|.

2. |x| - 4x = 15

Again, consider two cases based on the sign of x.

Case 1: x is positive. x - 4x = 15 Solve for x: -x = 15 x = -15 (However, this value is not positive, so it is not valid for this case.)

Case 2: x is negative. -(-x) - 4(-x) = 15 x + 4x = 15 5x = 15 x = 15/5 x = 3

So, the solution to the equation |x| - 4x = 15 is x = 3.

To summarize:

1. The solution to the equation |3x - 4| = |x - 6| is x = -1.
2. The solution to the equation |x| - 4x = 15 is x = 3.