Question

2) 3^x + 9 – |9 – 3^x| = |x – 6| +x​

Answer 1

Ответ:

Объяснение:

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Answer 2

To solve the equation 3^x + 9 – |9 – 3^x| = |x – 6| + x, we'll consider different cases based on the absolute values involved. Let's break it down:

Case 1: (9 - 3^x) ≥ 0 and (x - 6) ≥ 0 In this case, the absolute values on both sides of the equation simplify to their arguments. Therefore, we have: 3^x + 9 - (9 - 3^x) = x - 6 + x 3^x + 9 - 9 + 3^x = 2x - 6 2 * 3^x = 2x - 6 3^x = x - 6

Case 2: (9 - 3^x) ≥ 0 and (x - 6) < 0 Here, the absolute value on the left side remains as an absolute value, but on the right side, it changes the sign of its argument. Thus, we have: 3^x + 9 - (9 - 3^x) = -(x - 6) + x 3^x + 9 - 9 + 3^x = 6 - x + x 2 * 3^x = 6 3^x = 3

Case 3: (9 - 3^x) < 0 and (x - 6) ≥ 0 Similar to Case 2, we flip the sign of the absolute value on the left side and keep the one on the right side unchanged: 3^x + 9 - (-(9 - 3^x)) = x - 6 + x 3^x + 9 + 9 - 3^x = 2x - 6 18 = 2x - 6 2x = 24 x = 12

Case 4: (9 - 3^x) < 0 and (x - 6) < 0 In this case, both absolute values change signs, resulting in: 3^x + 9 + (9 - 3^x) = -(x - 6) - x 3^x + 9 + 9 - 3^x = -x + 6 - x 18 = -2x + 6 2x = -12 x = -6

Therefore, the solutions to the equation are x = 3, x = 12, and x = -6.