Question

(4x-1)(x+2)<1-4x ПОМОГИТЕ РЕШИТЬ ПОЖАЛУЙСТА

Answer 1

1. Раскрываем скобки
4x^2+8x-x-2<1-4x
4x^2+7x-2<1-4x
2. Переносим всё в левую часть
4x^2+7x-2-1+4x<0
4x^2+11x-3<0
D=11^2-4*4*(-3)=121+48=169
x1=(-11+13)/8=2/8=1/4=0,25
x2=(-11-13)/8=-24/8=-3
4x^2+11x-3=4(x-0,25)(x+3)
4(x-0,25)(x+3)<0
И по методу интервалов получается, что x принадлежит (-3;0,25)

Answer 2

I can help you with math problems. To solve this inequality, you need to expand the brackets, collect the terms, and find the values of x that satisfy the condition. Here are the steps:

- Expand the brackets: $(4x-1)(x+2)<1-4x$ - Simplify the left side: $4x^2+7x-2<1-4x$ - Move all the terms to one side: $4x^2+11x-3<0$ - Factor the quadratic expression: $(4x-1)(x+3)<0$ - Find the critical points: $x=\frac{1}{4}$ or $x=-3$ - Use a sign chart to determine the intervals where the expression is negative: $(-3,\frac{1}{4})$ - Write the final answer: $x\in(-3,\frac{1}{4})$

You can also use online calculators to check your answer or get more explanations. Here are some links:

- [Mathway | Решение задач по алгебре](https://www.mathway.com/ru/Algebra) - [Калькулятор Уравнений - Symbolab](https://ru.symbolab.com/solver/equation-calculator) - [Step-by-Step Math Problem Solver](https://quickmath.com/solve/)

I hope this helps. Have a nice day!