Question

A) |3x|=12 Б) |х+2|=-2 В) |х-3|=8

Answer 1

Ответ:

І3хІ=12

х=+-4

Іх+2І=-2

Нету розвязков

Іх-3І=8

х=11 x=-5

Answer 2

Let's solve each of the absolute value equations:

A) |3x| = 12

To solve this equation, we need to consider two cases: one when the expression inside the absolute value is positive and another when it's negative.

Case 1: 3x is positive If 3x is positive, the equation becomes: 3x = 12

Now, solve for x: x = 12/3 x = 4

Case 2: 3x is negative If 3x is negative, the equation becomes: -3x = 12

Now, solve for x: x = -12/3 x = -4

So, the solutions for the equation |3x| = 12 are x = 4 and x = -4.

B) |x + 2| = -2

It's important to note that the absolute value of any real number is always non-negative, which means it cannot be negative. Therefore, there are no real solutions to this equation. The equation |x + 2| = -2 has no solutions.

C) |x - 3| = 8

Again, we need to consider two cases: one when x - 3 is positive and another when it's negative.

Case 1: x - 3 is positive If x - 3 is positive, the equation becomes: x - 3 = 8

Now, solve for x: x = 8 + 3 x = 11

Case 2: x - 3 is negative If x - 3 is negative, the equation becomes: -(x - 3) = 8

Now, solve for x: -x + 3 = 8 -x = 8 - 3 -x = 5

Remember to flip the sign when isolating x: x = -5

So, the solutions for the equation |x - 3| = 8 are x = 11 and x = -5.