Question

2) |x - 4| < 3;4) |x+3| > 2;​

Answer 1

Ответ:

Відповідь на запитання

2) (7-4) < 3

4) (5+3) > 2

Answer 2

Sure, I can help you solve these absolute value inequalities.

2. |x - 4| < 3:

To solve this inequality, you can split it into two cases because the absolute value can make the expression positive or negative:

Case 1: x - 4 is positive (x - 4 > 0): x - 4 < 3 Add 4 to both sides: x < 7

Case 2: x - 4 is negative (x - 4 < 0): -(x - 4) < 3 Multiply both sides by -1 (and reverse the inequality): x - 4 > -3 Add 4 to both sides: x > 1

So, the solution to the inequality is: 1 < x < 7

4. |x + 3| > 2:

Again, you'll split this inequality into two cases:

Case 1: x + 3 is positive (x + 3 > 0): x + 3 > 2 Subtract 3 from both sides: x > -1

Case 2: x + 3 is negative (x + 3 < 0): -(x + 3) > 2 Multiply both sides by -1 (and reverse the inequality): x + 3 < -2 Subtract 3 from both sides: x < -5

So, the solution to the inequality is: x < -5 or x > -1