Question

1. |x|+3x=12 2. |x|-4x=9 3. 2(x-5)-6|x|=-18

Answer 1

Ответ:

1)x=3

2)x=1.5

3)x1=-1 x2=2

Объяснение:

1)x=3

2)x=1.5

3)x1=-1 x2=2

Answer 2

It looks like you have three equations involving absolute value expressions and variable x. You want to solve for the values of x that satisfy each equation. Let's go through them one by one:

1. |x| + 3x = 12:

To solve this equation, we'll need to consider two cases for the absolute value:

Case 1: x is positive or zero (x ≥ 0): In this case, |x| simplifies to just x. So the equation becomes: x + 3x = 12 4x = 12 x = 12 / 4 x = 3

Case 2: x is negative (x < 0): In this case, |x| simplifies to -x. So the equation becomes: -x + 3x = 12 2x = 12 x = 12 / 2 x = 6

So, the solutions for this equation are x = 3 and x = 6.

2. |x| - 4x = 9:

Again, we'll consider two cases:

Case 1: x is positive or zero (x ≥ 0): |x| simplifies to x, and the equation becomes: x - 4x = 9 -3x = 9 x = -9 / 3 x = -3

Case 2: x is negative (x < 0): |x| simplifies to -x, and the equation becomes: -x - 4x = 9 -5x = 9 x = -9 / 5

So, the solutions for this equation are x = -3 and x = -9/5.

3. 2(x - 5) - 6|x| = -18:

Here, we'll also consider two cases for the absolute value:

Case 1: x is positive or zero (x ≥ 0): |x| simplifies to x, and the equation becomes: 2(x - 5) - 6x = -18 2x - 10 - 6x = -18 -4x - 10 = -18 -4x = -18 + 10 -4x = -8 x = -8 / -4 x = 2

Case 2: x is negative (x < 0): |x| simplifies to -x, and the equation becomes: 2(x - 5) + 6x = -18 2x - 10 + 6x = -18 8x - 10 = -18 8x = -18 + 10 8x = -8 x = -8 / 8 x = -1

So, the solutions for this equation are x = 2 and x = -1.

Please double-check the calculations to make sure there are no errors, as solving equations involves several steps.