Question

|x-4|=2 |2-3x|=0 |3x+1|+2=8​

Answer 1

Ответ:

1. х=6
2. х=2/3
3. х=1$\frac{2}{3}$

Answer 2

To solve the absolute value equations, we'll consider each one separately:

1. |x - 4| = 2

To solve this equation, you'll have two cases:

Case 1: x - 4 = 2 x = 2 + 4 x = 6

Case 2: -(x - 4) = 2 -x + 4 = 2 -x = 2 - 4 -x = -2 x = 2 (Note: When you multiply both sides by -1, the inequality sign reverses.)

So, there are two solutions for this equation: x = 6 and x = 2.

2. |2 - 3x| = 0

An absolute value of a real number is always non-negative, and the absolute value of a real number is only equal to 0 when the number inside the absolute value bars is 0. So:

2 - 3x = 0

Now, solve for x:

-3x = -2 x = (-2) / (-3) x = 2/3

So, the solution to this equation is x = 2/3.

3. |3x + 1| + 2 = 8

First, subtract 2 from both sides of the equation:

|3x + 1| = 8 - 2 |3x + 1| = 6

Now, you have two cases:

Case 1: 3x + 1 = 6

Subtract 1 from both sides:

3x = 6 - 1 3x = 5

Divide by 3:

x = 5/3

Case 2: -(3x + 1) = 6

First, distribute the negative sign:

-3x - 1 = 6

Add 1 to both sides:

-3x = 6 + 1 -3x = 7

Divide by -3:

x = 7 / -3 x = -7/3

So, there are two solutions for this equation: x = 5/3 and x = -7/3.