Question

|2х-3|>4 решите неравенство​

Answer 1

$\left \{ {{2x-3>4} \atop {2x-37} \atop {2x3.5} \atop {x$

x∈(-∞;-0.5)(3.5;∞)

Answer 2

To solve the absolute value inequality |2x - 3| > 4, we need to consider two cases: one when the expression inside the absolute value is positive and another when it is negative. Let's solve each case separately:

Case 1: (2x - 3) > 4 Add 3 to both sides: 2x > 4 + 3 2x > 7 Now, divide both sides by 2 (since it's positive, we don't change the direction of the inequality): x > 7/2 x > 3.5

Case 2: -(2x - 3) > 4 Now, we need to change the direction of the inequality when we multiply/divide by a negative number: -2x + 3 > 4 Subtract 3 from both sides: -2x > 4 - 3 -2x > 1 Divide both sides by -2 (and change the direction of the inequality): x < 1/(-2) x < -1/2

So, we have two separate solutions for x: x > 3.5 and x < -1/2.

To express the final solution in interval notation, we combine the two separate intervals:

Solution: x ∈ (-∞, -1/2) ∪ (3.5, ∞)

This means any value of x that is less than -1/2 or greater than 3.5 will satisfy the original inequality.