Question

1) 7 < 2x + 3 <11; <4;8 + x3) -2 <72x + 14) -7922) -3 <1 + 2x < 7;

Answer 1

$-7$

Пошаговое объяснение:

что смогу понять то напишу

7<2x+3<11

4<2x<8

2<x<4

x принадлежит  (2;4)

-2<8+x<4

-10<x<-4

x принадлежит (-10;-4)

-3<1+2x<7

-4<2x<6

-2<x<3

x принадлежит (-2;3)

Остальное не понятно

Answer 2

To solve the system of inequalities, let's work through each inequality step by step and find the possible values for $x$ that satisfy them.

1. $7 < 2x + 3 < 11$: Subtract 3 from all parts of the inequality: $4 < 2x < 8$ Now, divide by 2: $2 < x < 4$

2. $-2 < 7(2x + 1) - 7 < 22$: Simplify the expression inside the parentheses: $-2 < 14x + 7 - 7 < 22$ $-2 < 14x < 22$ Now, divide by 14: $-\frac{1}{7} < x < \frac{11}{7}$

3. $-3 < 1 + 2x < 7$: Subtract 1 from all parts of the inequality: $-4 < 2x < 6$ Now, divide by 2: $-2 < x < 3$

Now, let's find the intersection of these ranges for $x$:

• The common range between 1) and 2) is $2 < x < 4$.
• The common range between 1) and 3) is $-2 < x < 3$.

Combining these, the valid range for $x$ that satisfies all three inequalities is $2 < x < 3$.