Question

1)|х|=6; 2)|-х|=7; 3)|4х|=8; 4)|5х|=3; 5)|х+1|=4 6)|х|+3=7​

Answer 1

1) х = -6 или х = 6.

2) -х = -7 или -х =7

х =7 или х=-7.

3) 4х =-8 или 4х = 8

х = -2 или х = 2.

4) 5х = -3 или 5х =3,

х = -3/5 или х = 3/5.

5) х+1=-4 или х+1=4

х =-5 или х = 3.

6) |х| = 4

х =-4 или х= 4.

Answer 2

To solve each absolute value equation, we need to consider two cases for each equation. Remember that the absolute value of a number is its distance from zero, so it can be either positive or negative. Let's go through each equation step by step:

1. |х| = 6: Case 1: х = 6 Case 2: х = -6

2. |-х| = 7: Case 1: -х = 7 х = -7 (Remember to flip the sign when moving the absolute value to the other side.) Case 2: -(-х) = 7 х = 7 (Removing the double negative)

3. |4х| = 8: Case 1: 4х = 8 х = 2 Case 2: -4х = 8 х = -2

4. |5х| = 3: Case 1: 5х = 3 х = 3/5 Case 2: -5х = 3 х = -3/5

5. |х + 1| = 4: Case 1: х + 1 = 4 х = 4 - 1 х = 3 Case 2: -(х + 1) = 4 х + 1 = -4 х = -4 - 1 х = -5

6. |х| + 3 = 7: Case 1: х = 7 - 3 х = 4 Case 2: -х = 7 - 3 х = -4

So the solutions to each equation are as follows:

1. х = 6 or х = -6
2. х = 7 or х = -7
3. х = 2 or х = -2
4. х = 3/5 or х = -3/5
5. х = 3 or х = -5
6. х = 4 or х = -4