Question

1)-2<3х+1<7 2)2<5х-3<17 3)3<7-4х<15 4)-12<2(х+3)<4​

Answer 1

Пошаговое объяснение:

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

3x+1>-2; 3x>-2-1; x>-3/3; x>-1

3x+1<7; 3x<7-1; x<6/3; x<2

x принадлежит (-1; 2)

2). 2<5x-3<17

5x-3>2; 5x>3+2; x>5/5; x>1

5x-3<17; 5x<17+3; x<20/5; x<4

x принадлежит (1; 4)

3). 3<7-4x<15

7-4x>3; 4x<7-3; x<4/4; x<1

7-4x<15; 4x>7-15; x>-8/4; x>-2

x принадлежит (-2; 1).

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

-6<x+3<2

x+3>-6; x>-6-3; x>-9

x+3<4; x<4-3; x<1

x принадлежит (-9; 1)

Answer 2

To solve each of the inequalities, we'll isolate the variable "x" step-by-step. Remember that when you perform operations (adding, subtracting, multiplying, or dividing) on an inequality, you must do the same operation to all parts of the inequality to maintain its balance. Here's how to solve each of the given inequalities:

1. -2 < 3x + 1 < 7

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

Step 2: Divide by 3 (since the coefficient of x is 3) on all parts of the inequality: -1 < x < 2

So, the solution for this inequality is: -1 < x < 2.

2. 2 < 5x - 3 < 17

Step 1: Add 3 to all parts of the inequality: 5 < 5x < 20

Step 2: Divide by 5 (since the coefficient of x is 5) on all parts of the inequality: 1 < x < 4

So, the solution for this inequality is: 1 < x < 4.

3. 3 < 7 - 4x < 15

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

Step 2: Divide by -4 (note that when you divide by a negative number, the inequality direction reverses) on all parts of the inequality: 1 > x > -2

So, the solution for this inequality is: -2 < x < 1.

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

Step 1: Divide by 2 on all parts of the inequality: -6 < x + 3 < 2

Step 2: Subtract 3 from all parts of the inequality: -9 < x < -1

So, the solution for this inequality is: -9 < x < -1.

Keep in mind that these solutions represent the range of values for the variable "x" that satisfy the given inequalities.