Question

1) |x - 4) = 2; 2) |y + 5|= 3;3) |3 + x|= 1,5;4) |17 - y| = -2;5) |x +3|+ 4 = 9;6) |y - 2|+ 8 = 5.​

Answer 1

Ответ:

1)|х-4|=2

|х|=2+4

|х|=6

х=6

2)|у+5|=3

|у|=3-5

у=-2

3)|3+х|=1,5

|х|=1,5-3

|х|=-1,5

4)|17-у|=-2

|у|=-2-17

|у|=-19

у=19

5)|х+3|+4=9

|х+3|=9-4

|х+3|=5

|х|=5-3

|х|=2

х=2

6)|у-2|+8=5

|у-2|=5-8

|у-2|=-3

|у|=-3+2

|у|=-1

у=1

Answer 2

To solve each of these absolute value equations, you'll need to consider two cases: one where the expression inside the absolute value is positive, and another where it is negative (or zero). Here's how to solve each equation:

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

   Case 2: -(x - 4) = 2 (since the absolute value can also be negative) -x + 4 = 2 -x = 2 - 4 -x = -2 x = 2

So, the solutions are x = 6 and x = 2.

2. |y + 5| = 3: Case 1: y + 5 = 3 y = 3 - 5 y = -2

   Case 2: -(y + 5) = 3 -y - 5 = 3 -y = 3 + 5 -y = 8 y = -8

So, the solutions are y = -2 and y = -8.

3. |3 + x| = 1.5: Case 1: 3 + x = 1.5 x = 1.5 - 3 x = -1.5

   Case 2: -(3 + x) = 1.5 -3 - x = 1.5 -x = 1.5 + 3 -x = 4.5 x = -4.5

So, the solutions are x = -1.5 and x = -4.5.

4. |17 - y| = -2: Absolute values cannot be negative, so there are no real solutions to this equation.

5. |x + 3| + 4 = 9: First, subtract 4 from both sides: |x + 3| = 9 - 4 |x + 3| = 5

   Case 1: x + 3 = 5 x = 5 - 3 x = 2

   Case 2: -(x + 3) = 5 -x - 3 = 5 -x = 5 + 3 -x = 8 x = -8

So, the solutions are x = 2 and x = -8.

6. |y - 2| + 8 = 5: First, subtract 8 from both sides: |y - 2| = 5 - 8 |y - 2| = -3

Since absolute values cannot be negative, there are no real solutions to this equation.

In summary, the solutions to the given absolute value equations are as follows:

1. x = 6 and x = 2
2. y = -2 and y = -8
3. x = -1.5 and x = -4.5
4. No real solutions
5. x = 2 and x = -8
6. No real solutions