Question

1<5+х/2<2,5 2)0<2х+3/5<1​

Answer 1

Пошаговое объяснение:

1)

1<5+x/2<2,5   |-5

-4<x/2<-2,5  |*2

-8<x<-5

x∈(-8;-5)

2)

0<2x+3/5<1  |-3/5

-3/5<2x<2/5

-0,3<x<0,2

x∈(-0,3;0,2)

Answer 2

To solve the inequalities, we will work on them one by one:

1. 1 < 5 + x/2 < 2.5

Let's start by subtracting 5 from all parts of the inequality:

1 - 5 < 5 + x/2 - 5 < 2.5 - 5

Simplifying:

-4 < x/2 < -2.5

Next, multiply all parts of the inequality by 2 to eliminate the fraction:

-4 * 2 < (x/2) * 2 < -2.5 * 2

-8 < x < -5

So the solution for the first inequality is -8 < x < -5.

2. 0 < 2x + 3/5 < 1

Let's start by subtracting 3/5 from all parts of the inequality:

0 - 3/5 < 2x + 3/5 - 3/5 < 1 - 3/5

Simplifying:

-3/5 < 2x < 2/5

Next, divide all parts of the inequality by 2 to isolate x:

(-3/5) / 2 < (2x) / 2 < (2/5) / 2

-3/10 < x < 1/5

So the solution for the second inequality is -3/10 < x < 1/5.

Therefore, the combined solution for both inequalities is:

-8 < x < -5 and -3/10 < x < 1/5.