Question

-1 < 3-2x/5 <(или равно) 9

Answer 1

-1 < (3-2x)/5 ≤ 9

-5 < 3-2x ≤ 45

-8 < -2x ≤ 42

4 > x ≥ -21

-21 ≤ x < 4

x ∈ [-21;4)

Answer 2

$-1-1\\\\\frac{3-2x}{5} \leq 9\\\\x$∈[-21; 4)

Answer 3

To solve the compound inequality -1 < (3 - 2x/5) ≤ 9, we'll break it down into two separate inequalities and solve them individually.

First, let's solve the left inequality: -1 < (3 - 2x/5).

-1 < 3 - 2x/5

To isolate the variable x, we'll subtract 3 from both sides:

-1 - 3 < -2x/5

-4 < -2x/5

To get rid of the fraction, we'll multiply both sides by 5:

-4 * 5 < -2x

-20 < -2x

Now, divide both sides by -2. Since we're dividing by a negative number, the inequality sign will flip:

-20 / -2 > x

10 > x

So the left inequality is x < 10.

Now, let's solve the right inequality: (3 - 2x/5) ≤ 9.

(3 - 2x/5) ≤ 9

To isolate the variable x, we'll subtract 3 from both sides:

(3 - 2x/5) - 3 ≤ 9 - 3

-2x/5 ≤ 6

Next, we'll multiply both sides by 5 to eliminate the fraction:

5 * (-2x/5) ≤ 6 * 5

-2x ≤ 30

Now, divide both sides by -2. Since we're dividing by a negative number, the inequality sign will flip:

-2x / -2 ≥ 30 / -2

x ≥ -15

So the right inequality is x ≥ -15.

Combining the results from the left and right inequalities, we have:

x < 10 and x ≥ -15.

In interval notation, the solution is (-∞, 10) ∪ [-15, +∞).