Question

|x| + 5 = 2|х + 12| = 3

Answer 1

|x| + 5 = 2

|x| = -3

модуль отрицательным быть не может значит нет решений

|х + 12| = 3

х + 12 = 3 или х+12=-3

х = -9 или х=-15

Answer 2

To solve the given equation, we need to find the possible values of x that satisfy the equation. We'll tackle it step by step.

Step 1: Break the equation into two separate equations based on the absolute value.

1. |x| + 5 = 3
2. |x + 12| = 3

Step 2: Solve each equation separately.

Equation 1: |x| + 5 = 3

Subtract 5 from both sides:

|x| = 3 - 5 |x| = -2

An absolute value cannot be negative, so there are no solutions for this part of the equation.

Equation 2: |x + 12| = 3

We have two cases to consider for the absolute value:

Case 1: x + 12 = 3 Subtract 12 from both sides: x = 3 - 12 x = -9

Case 2: -(x + 12) = 3 First, distribute the negative sign: -x - 12 = 3

Now, add 12 to both sides: -x = 3 + 12 -x = 15

Finally, multiply both sides by -1 (to solve for x): x = -15

Step 3: Check the solutions.

We have two potential solutions: x = -9 and x = -15. We need to check if they satisfy the original equation.

For x = -9: |x| + 5 = 2|x + 12| = 3 |-9| + 5 = 2|-9 + 12| = 3 9 + 5 = 2|3| = 3 14 = 2 * 3 = 3

The equation doesn't hold true for x = -9.

For x = -15: |x| + 5 = 2|x + 12| = 3 |-15| + 5 = 2|-15 + 12| = 3 15 + 5 = 2| -3 | = 3 20 = 2 * 3 = 3

Again, the equation doesn't hold true for x = -15.

Step 4: Conclusion.

After checking both potential solutions, we find that neither of them satisfies the given equation. Therefore, there are no real solutions to the equation |x| + 5 = 2|x + 12| = 3.