Question

||x|+4|=1 2|x|+3=13 |1-7x|-4=-4

Answer 1

Ответ:

решение на фотографии

Answer 2

To solve the given absolute value equations, you'll need to consider both the positive and negative cases for the absolute value. Here's how you can solve each equation:

1. |x| + 4 = 12

First, isolate the absolute value expression:

|x| = 12 - 4 |x| = 8

Now, you have two cases:

Case 1: x is positive: x = 8

Case 2: x is negative: -x = 8 x = -8

So, there are two solutions: x = 8 and x = -8.

2. 2|x| + 3 = 13

Isolate the absolute value expression:

2|x| = 13 - 3 2|x| = 10

Now, divide by 2:

|x| = 5

Again, you have two cases:

Case 1: x is positive: x = 5

Case 2: x is negative: -x = 5 x = -5

So, there are two solutions: x = 5 and x = -5.

3. |1 - 7x| - 4 = -4

First, add 4 to both sides of the equation:

|1 - 7x| = 0

Now, you have two cases:

Case 1: 1 - 7x is positive: 1 - 7x = 0 -7x = -1 x = 1/7

Case 2: 1 - 7x is negative: -(1 - 7x) = 0 -1 + 7x = 0 7x = 1 x = 1/7

In this case, both cases lead to the same solution: x = 1/7.

So, the solutions to the given equations are:

1. x = 8 or x = -8
2. x = 5 or x = -5
3. x = 1/7