Question

Решите |-4| + |1 - 3x|

Answer 1

...............

4 + |1-3x|

Answer 2

To solve the expression |-4| + |1 - 3x|, we need to compute the absolute values first and then perform the addition.

1. Calculate |-4|: The absolute value of -4 is simply 4: |-4| = 4.

2. Calculate |1 - 3x|: The absolute value of (1 - 3x) depends on the value of (1 - 3x).

For (1 - 3x) ≥ 0: |1 - 3x| = (1 - 3x)

For (1 - 3x) < 0: |1 - 3x| = -(1 - 3x) = 3x - 1

Now, we need to find the point where (1 - 3x) changes its sign from non-negative to negative, which is when (1 - 3x) = 0:

1 - 3x = 0 3x = 1 x = 1/3

Therefore, when x < 1/3, |1 - 3x| = 3x - 1, and when x ≥ 1/3, |1 - 3x| = 1 - 3x.

3. Combine the absolute values: To summarize, we have: For x < 1/3: |1 - 3x| = 3x - 1 For x ≥ 1/3: |1 - 3x| = 1 - 3x

4. Evaluate the expression:

Let's consider the cases:

Case 1: x < 1/3 |-4| + |1 - 3x| = 4 + (3x - 1) = 3x + 3

Case 2: x ≥ 1/3 |-4| + |1 - 3x| = 4 + (1 - 3x) = 5 - 3x

So, the final expression will be:

3x + 3 for x < 1/3 5 - 3x for x ≥ 1/3