Question

2(x-5) - 6 /x/=-18 ДАЮ 10 БАЛЛОВ ​

Answer 1

Объяснение:

2x-10-6x=-18 если x > 0

Тогда

-4x=-8

x=2

Или если x<0

2x-10+6x=-18

8x=8

X=1

2

Answer 2

To solve the equation 2(x-5) - 6 / |x| = -18, we need to consider two cases for the absolute value of x: x ≥ 0 and x < 0.

Case 1: x ≥ 0

When x is greater than or equal to 0, the absolute value of x is just x. So the equation becomes:

2(x - 5) - 6 / x = -18

Step 1: Eliminate the fraction by multiplying everything by x to get rid of the denominator:

2(x - 5)x - 6 = -18x

Step 2: Expand and simplify:

2x^2 - 10x - 6 = -18x

Step 3: Move all terms to one side to set the equation to zero:

2x^2 - 10x - 6 + 18x = 0

Step 4: Combine like terms:

2x^2 + 8x - 6 = 0

Step 5: Solve the quadratic equation. Factoring is usually the easiest method:

2(x^2 + 4x - 3) = 0

Now, solve the quadratic factor:

x^2 + 4x - 3 = 0

(x + 3)(x - 1) = 0

Now, set each factor to zero and solve for x:

x + 3 = 0 or x - 1 = 0

Case 1.1: x + 3 = 0

x = -3

Case 1.2: x - 1 = 0

x = 1

So for the first case, x can be either -3 or 1.

Case 2: x < 0

When x is less than 0, the absolute value of x is -x. So the equation becomes:

2(x - 5) - 6 / (-x) = -18

Step 1: Eliminate the fraction by multiplying everything by -x to get rid of the denominator:

2(x - 5)(-x) - 6 = -18(-x)

Step 2: Expand and simplify:

-2x^2 + 10x - 6 = 18x

Step 3: Move all terms to one side to set the equation to zero:

-2x^2 + 10x - 6 - 18x = 0

Step 4: Combine like terms:

-2x^2 - 8x - 6 = 0

Step 5: Solve the quadratic equation. Factoring is usually the easiest method:

-2(x^2 + 4x + 3) = 0

Now, solve the quadratic factor:

x^2 + 4x + 3 = 0

(x + 3)(x + 1) = 0

Now, set each factor to zero and solve for x:

x + 3 = 0 or x + 1 = 0

Case 2.1: x + 3 = 0

x = -3

Case 2.2: x + 1 = 0

x = -1

So for the second case, x can be either -3 or -1.

Final Solutions:

The equation has four possible solutions: x = -3, x = -1, x = 1, or x = 3.

I hope this explanation helps! If you have any further questions, feel free to ask.