Question

|x|+6=13 7|x|-3=0|x|-7 = -12|х-5| = 4|9+х|=0|x-4|=2|3x +4|=2|2x +1|+13= 14​

Answer 1

Ответ:

1) 7

2) 3/7

4) 9

5) -9

6) 6

7) -2/3

8) 0

Answer 2

Let's solve each of these absolute value equations one by one:

1. |x| + 6 = 13: First, subtract 6 from both sides: |x| = 13 - 6 |x| = 7

   Now, consider two cases: Case 1: x is positive: x = 7

   Case 2: x is negative: x = -7

   So, there are two solutions: x = 7 and x = -7.

2. 7|x| - 3 = 0: Add 3 to both sides: 7|x| = 3

   Now, divide both sides by 7: |x| = 3/7

   Again, consider two cases: Case 1: x is positive: x = 3/7

   Case 2: x is negative: x = -3/7

   So, there are two solutions: x = 3/7 and x = -3/7.

3. |x - 7| = -12: The absolute value of any real number is never negative, so there are no solutions to this equation.

4. |x - 5| = 4: Consider two cases: Case 1: x - 5 is positive or zero: x - 5 = 4 Add 5 to both sides: x = 4 + 5 x = 9

   Case 2: x - 5 is negative: -(x - 5) = 4 Multiply both sides by -1: x - 5 = -4 Add 5 to both sides: x = -4 + 5 x = 1

   So, there are two solutions: x = 9 and x = 1.

5. |9 + x| = 0: The absolute value of any real number is never negative, so there is only one solution: 9 + x = 0 Subtract 9 from both sides: x = -9

6. |x - 4| = 2: Consider two cases: Case 1: x - 4 is positive or zero: x - 4 = 2 Add 4 to both sides: x = 2 + 4 x = 6

   Case 2: x - 4 is negative: -(x - 4) = 2 Multiply both sides by -1: x - 4 = -2 Add 4 to both sides: x = -2 + 4 x = 2

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

7. |3x + 4| = 2: Consider two cases: Case 1: 3x + 4 is positive or zero: 3x + 4 = 2 Subtract 4 from both sides: 3x = 2 - 4 3x = -2 Divide by 3: x = -2/3

   Case 2: 3x + 4 is negative: -(3x + 4) = 2 Multiply both sides by -1: 3x + 4 = -2 Subtract 4 from both sides: 3x = -2 - 4 3x = -6 Divide by 3: x = -6/3 x = -2

   So, there are two solutions: x = -2/3 and x = -2.