Question

1)-2<3x+1<7;2) 2<5x-3<17;​

Answer 1

Ответ:

1)-1<x<2

2)1<x<4

...............

Answer 2

To solve these compound inequalities, you'll need to isolate the variable x in each of them. Let's work through them one by one:

1. -2 < 3x + 1 < 7

First, subtract 1 from all parts of the inequality:

-2 - 1 < 3x + 1 - 1 < 7 - 1

Simplify:

-3 < 3x < 6

Now, divide each part by 3 to isolate x:

(-3) / 3 < (3x) / 3 < 6 / 3

Simplify further:

-1 < x < 2

So, the solution to the first inequality is: -1 < x < 2.

2. 2 < 5x - 3 < 17

First, add 3 to all parts of the inequality:

2 + 3 < 5x - 3 + 3 < 17 + 3

Simplify:

5 < 5x < 20

Now, divide each part by 5 to isolate x:

(5) / 5 < (5x) / 5 < (20) / 5

Simplify further:

1 < x < 4

So, the solution to the second inequality is: 1 < x < 4.