Question

1)|x|+3=5, 2)|2x|+3=9 3)3/7+|4x|=1​

Answer 1

ОТВЕТ

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1) |х|+3=5

х¹= –2. х²= 5

2) |2х|+3=8

х¹= –3. х²= 3

3) 3/7+ |4х|=1

х¹= –1/7. х²= 1/7

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Желаю удачи.

Answer 2

To solve each of these absolute value equations, you'll need to consider two cases: one where the expression inside the absolute value is positive and one where it's negative. Let's solve each equation step by step:

1. |x| + 3 = 5:

Case 1 (x is positive): x + 3 = 5 x = 5 - 3 x = 2

Case 2 (x is negative):

• x + 3 = 5
• x = 5 - 3
• x = 2

So, the solutions to this equation are x = 2 and x = -2.

2. |2x| + 3 = 9:

Case 1 (2x is positive): 2x + 3 = 9 2x = 9 - 3 2x = 6 x = 6/2 x = 3

Case 2 (2x is negative): -2x + 3 = 9 -2x = 9 - 3 -2x = 6 x = 6/(-2) x = -3

The solutions to this equation are x = 3 and x = -3.

3. (3/7) + |4x| = 1:

First, isolate the absolute value term:

|4x| = 1 - 3/7

|4x| = (7/7) - (3/7) |4x| = 4/7

Now, consider the two cases:

Case 1 (4x is positive): 4x = 4/7 x = (4/7) / 4 x = 1/7

Case 2 (4x is negative): -4x = 4/7 x = -(4/7) / 4 x = -(1/7)

So, the solutions to this equation are x = 1/7 and x = -1/7.