Question

1) -2<3x+1<7;2) 2<5x-3<17;3) 3<7-4x<15;4) -12 2(x+3)<4.​

Answer 1

Ответ:

1) -3<3х<6

-1<х<2

2) 5<5х<20

1<х<4

3) -4<-4х<8

4>4х>-8

1>х>-2

-2<х<1

Answer 2

To solve each of these inequalities, we'll follow the standard procedures for isolating the variable on one side of the inequality sign. Let's solve each inequality step by step:

1. -2 < 3x + 1 < 7

Step 1: Subtract 1 from all parts of the inequality: -2 - 1 < 3x + 1 - 1 < 7 - 1 -3 < 3x < 6

Step 2: Divide by 3 (since the coefficient of x is 3 and we want to isolate x): -3 / 3 < 3x / 3 < 6 / 3 -1 < x < 2

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

2. 2 < 5x - 3 < 17

Step 1: Add 3 to all parts of the inequality: 2 + 3 < 5x - 3 + 3 < 17 + 3 5 < 5x < 20

Step 2: Divide by 5 (since the coefficient of x is 5 and we want to isolate x): 5 / 5 < 5x / 5 < 20 / 5 1 < x < 4

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

3. 3 < 7 - 4x < 15

Step 1: Subtract 7 from all parts of the inequality: 3 - 7 < 7 - 4x - 7 < 15 - 7 -4 < -4x < 8

Step 2: Divide by -4 (and remember that when dividing by a negative number, the inequality sign flips): -4 / -4 > -4x / -4 > 8 / -4 1 > x > -2

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

4. -12 < 2(x + 3) < 4

Step 1: Simplify inside the parentheses: -12 < 2x + 6 < 4

Step 2: Subtract 6 from all parts of the inequality: -12 - 6 < 2x + 6 - 6 < 4 - 6 -18 < 2x < -2

Step 3: Divide by 2: -18 / 2 < 2x / 2 < -2 / 2 -9 < x < -1

So, the solution to the fourth inequality is -9 < x < -1.