Question

2) ||x|-7|=5. 3) ||x|-10|=2

Answer 1

Ответ:

Пошаговое объяснение:

2) |x|-7=5; |x|=12; x1=12 x2=-12

   |x|-7=-5; |x|=2; x3=2 x4=-2

3) |x|-10=2; |x|=12; x1=12 x2=-12

   |x|-10=-2; |x|=8; x3=8 x4=-8

Answer 2

To solve these absolute value equations, we'll consider the two possible cases for each equation.

Case 1: (x - 7) is positive: In this case, we have: |x| - 7 = 5

Adding 7 to both sides: |x| = 12

Since (x - 7) is positive, x must be greater than 7. Thus, the equation simplifies to: x = 12

Case 2: (x - 7) is negative: In this case, we have: -(x - 7) = 5

Expanding the equation: -x + 7 = 5

Subtracting 7 from both sides: -x = -2

Multiplying both sides by -1 (to get x by itself): x = 2

Therefore, the solutions for the equation ||x| - 7| = 5 are x = 2 and x = 12.

Now let's solve the second equation:

Case 1: (x - 10) is positive: In this case, we have: |x| - 10 = 2

Adding 10 to both sides: |x| = 12

Since (x - 10) is positive, x must be greater than 10. Thus, the equation simplifies to: x = 12

Case 2: (x - 10) is negative: In this case, we have: -(x - 10) = 2

Expanding the equation: -x + 10 = 2

Subtracting 10 from both sides: -x = -8

Multiplying both sides by -1 (to get x by itself): x = 8

Therefore, the solutions for the equation ||x| - 10| = 2 are x = 8 and x = 12.