Question

1) (7 |2X| -5 ) :2=1 2) -(-X)=7,8 3)|-X|=-0,01 4) 2/3 |X|=1,4

Answer 1

Пошаговое объяснение:

(7|2х| - 5) : 2 = 1

7|2х| - 5 = 1 * 2

7|2х| - 5 = 2

7|2х| = 2 + 5

7|2х| = 7

|2х| = 7 : 7

|2х| = 1

2|х| = 1

|х| = 1 : 2

|х| = 0,5

х1 = -0,5

х2 = 0,5

2)

-(-х) = 7,8

+х = 7,8

х = 7,8

3)

|-х| = -0,01

|х| = -0,01

Нет корней, так как модуль числа всегда положительный или равен нулю.

х Є ∅

4)

2/3|х| = 1,4

|х| = 1,4 : 2/3

|х| = 14/10 * 3/2

|х| = 7/10 * 3/1

|х| = 21/10

|х| = 2,1

х1 = -2,1

х2 = 2,1

Answer 2

Let's solve each of the equations step by step:

1. (7 |2X| - 5) / 2 = 1

First, we isolate the absolute value term by adding 5 to both sides:

7 |2X| = 1 + 5

7 |2X| = 6

Next, we divide both sides by 7:

|2X| = 6 / 7

Now, we consider two cases: positive and negative solutions for |2X|.

Case 1: 2X is positive In this case, |2X| = 2X, so we have:

2X = 6 / 7

Divide both sides by 2:

X = (6 / 7) / 2

X = 6 / 14

Simplify the fraction:

X = 3 / 7

Case 2: 2X is negative In this case, |2X| = -2X, so we have:

-2X = 6 / 7

Divide both sides by -2:

X = (6 / 7) / -2

X = -6 / 14

Simplify the fraction:

X = -3 / 7

Therefore, the solutions to the equation are X = 3/7 and X = -3/7.

2. -(-X) = 7.8

Simplifying the left side of the equation:

-(-X) = X

The equation becomes:

X = 7.8

The solution to the equation is X = 7.8.

3. |-X| = -0.01

The absolute value of any number is always non-negative, so there is no solution to this equation. The equation |-X| = -0.01 has no valid solutions.

4. (2/3) |X| = 1.4

First, let's isolate the absolute value term by dividing both sides by (2/3):

|X| = 1.4 / (2/3)

To divide by a fraction, we can multiply by its reciprocal:

|X| = 1.4 * (3/2)

|X| = 2.1

Now, we consider two cases: positive and negative solutions for |X|.

Case 1: X is positive In this case, |X| = X, so we have:

X = 2.1

The solution is X = 2.1.

Case 2: X is negative In this case, |X| = -X, so we have:

-X = 2.1

Multiply both sides by -1:

X = -2.1

The solution is X = -2.1.

Therefore, the solutions to the equation are X = 2.1 and X = -2.1.