Question

Модуль 2x-4 больше либо равно 1

Answer 1

1) 2x - 4 ≥ 1

2x ≥ 5

x ≥ 2,5

2) 2x - 4 ≤ -1

2x ≤ 3

x ≤ 1,5

Ответ: x ∈ (-∞; 1,5] U [2,5; +∞)

Answer 2

To find the values of 'x' that make the expression 2x-4 greater than or equal to 1, we need to solve the inequality:

2x - 4 ≥ 1

Let's solve it step-by-step:

1. Add 4 to both sides of the inequality to isolate the term with 'x': 2x - 4 + 4 ≥ 1 + 4

Simplifying: 2x ≥ 5

2. Now, divide both sides by 2 to solve for 'x': 2x/2 ≥ 5/2

Simplifying: x ≥ 5/2

So, the solution to the inequality is x being greater than or equal to 2.5 (or 5/2). In interval notation, this can be represented as [2.5, +∞) where '+∞' denotes infinity. This means any value of 'x' greater than or equal to 2.5 will make the expression 2x-4 greater than or equal to 1.