Question

7|x|-2|x| = 3|x| + 12;​

Answer 1

7|x| -2|x|-3|x|=12

2|x|=12

|x|=12:2

|x|=6

x1 =-6 ; x2=6

Ответ: - 6;6

Answer 2

To solve the equation 7|x| - 2|x| = 3|x| + 12, we can consider the two cases: one where |x| is positive and another where |x| is negative. Let's solve for each case separately:

Case 1: |x| is positive

In this case, we can remove the absolute value symbols and solve the equation as follows:

7x - 2x = 3x + 12 (since |x| = x when x is positive)

Combining like terms:

5x = 3x + 12

Subtracting 3x from both sides:

2x = 12

Dividing both sides by 2:

x = 6

So, when |x| is positive, x = 6 is a solution.

Case 2: |x| is negative

In this case, we need to change the signs inside the absolute value symbols and solve the equation:

7(-x) - 2(-x) = 3(-x) + 12 (since |x| = -x when x is negative)

Simplifying:

-7x + 2x = -3x + 12

Combining like terms:

-5x = -3x + 12

Adding 3x to both sides:

-2x = 12

Dividing both sides by -2:

x = -6

So, when |x| is negative, x = -6 is a solution.

Therefore, the equation 7|x| - 2|x| = 3|x| + 12 has two solutions: x = 6 and x = -6.