Question

1537. Решите уравнения: 1) |x| = 7; 2) |2x| = 8; 1538. 3) |x + 1 = 3; 4) |x| = -5;

Answer 1

1. |x| = 7

To solve this equation, we consider two cases:

Case 1: x is positive. In this case, the equation |x| = 7 becomes x = 7. So, x = 7 is a solution.

Case 2: x is negative. In this case, the equation |x| = 7 becomes -x = 7. Solving for x, we have x = -7. Therefore, x = -7 is also a solution.

Therefore, the solutions to the equation |x| = 7 are x = 7 and x = -7.

2. |2x| = 8

Again, we consider two cases:

Case 1: 2x is positive. In this case, the equation |2x| = 8 becomes 2x = 8. Solving for x, we have x = 4.

Case 2: 2x is negative. In this case, the equation |2x| = 8 becomes -2x = 8. Solving for x, we have x = -4.

Therefore, the solutions to the equation |2x| = 8 are x = 4 and x = -4.

3. |x + 1| = 3

Again, we consider two cases:

Case 1: x + 1 is positive. In this case, the equation |x + 1| = 3 becomes x + 1 = 3. Solving for x, we have x = 2.

Case 2: x + 1 is negative. In this case, the equation |x + 1| = 3 becomes -(x + 1) = 3. Solving for x, we have x = -4.

Therefore, the solutions to the equation |x + 1| = 3 are x = 2 and x = -4.

4. |x| = -5

The absolute value of any number is always non-negative, so it cannot be equal to a negative value. Therefore, the equation |x| = -5 has no solutions.