Question

13(2x - 4)<2(2x + 3),{(x+2)(x - 5) <(x+3)(x - 5)​

Answer 1

Ответ:

x ∈ ( -∞; 29/11 )

x ∈ ( 5; +∞ )

Объяснение:

1) 13(2x - 4 )< 2(2x + 3)                       2) (x+2)(x - 5) <(x+3)(x - 5)​

26x - 52 < 4x + 6                                 x^2 - 5x + 2x - 10 < x^2 - 5x + 3x - 15

26x - 4x < 6 + 52                                 x^2 - 5x + 2x - 10 - x^2 + 5x - 3x + 15 < 0

22x < 58                                              Сокращаем:

x < 58 / 22                                           2x - 10 - 3x + 15 < 0

x < 29 / 11 (дробь)                               -x + 5 < 0

Ответ: x ∈ ( -∞; 29/11 )                        -x < -5

                                                              x > -5 / (-1)

                                                              x > 5

                                                             Ответ: x ∈( 5; +∞ )

Answer 2

To solve the inequality 13(2x - 4) < 2(2x + 3), we can start by simplifying it:

13(2x - 4) < 2(2x + 3)

Now, distribute the constants:

26x - 52 < 4x + 6

Next, let's isolate the variable x by moving all the terms containing x to one side of the inequality and the constants to the other side. Subtract 4x from both sides:

26x - 4x - 52 < 6

Combine like terms:

22x - 52 < 6

Now, add 52 to both sides to isolate the 22x:

22x - 52 + 52 < 6 + 52

22x < 58

Finally, divide by 22 to solve for x:

(22x) / 22 < 58 / 22

x < 29/11

So, the solution to the inequality 13(2x - 4) < 2(2x + 3) is:

x < 29/11

Now, let's solve the inequality {(x+2)(x - 5) < (x+3)(x - 5).

First, notice that (x - 5) is common to both sides, and you can cancel it out since it's not equal to zero:

(x + 2) < (x + 3)

Now, subtract x from both sides:

2 < 3

This inequality is always true, which means there are no restrictions on the values of x. In other words, any real number for x satisfies the inequality {(x+2)(x - 5) < (x+3)(x - 5).