Question

1) 17 + x < 5; 4) 2,6 - x > 1,1;2) (29-xl < 13;5) |x + 8,8| < 2,2;3) |х - 2,5| >3,5;6)|7,1 - х|> 8,2.​

Answer 1

Объяснение:

1) х< -12

4)х<1,5

2) |29-х|<13

система:

29-х<13

29-х> -13

система:

х>16

х<42

5)|х+8,8|<2,2

система:

x+8,8<2,2

х+8,8>-2,2

система:

х<-6,6

х>-11

3)|х - 2,5| >3,5

совокупность:

х-2,5>3,5

х-2,5<-3,5

совокупность:

х>6

х<-1

6)|7,1 - х|> 8,2

совокупность:

7,1-х>8,2

7,1-х<-8,2

совокупность:

х<-1,1

х>15,3

(я не менял неравенства местами)

Answer 2

To solve these inequalities, let's take them one by one:

1. 17 + x < 5: Subtract 17 from both sides to isolate x: x < 5 - 17 x < -12

2. 29 - x < 13: Subtract 29 from both sides to isolate x: -x < 13 - 29 -x < -16

Remember, when you multiply or divide both sides of an inequality by a negative number, the inequality sign flips. So, to get rid of the negative sign in front of x, multiply both sides by -1:

x > 16

3. |x - 2.5| > 3.5: This absolute value inequality breaks down into two separate inequalities:

x - 2.5 > 3.5 or x - 2.5 < -3.5

1st part: x - 2.5 > 3.5 Add 2.5 to both sides to isolate x: x > 3.5 + 2.5 x > 6

2nd part: x - 2.5 < -3.5 Add 2.5 to both sides to isolate x: x < -3.5 + 2.5 x < -1

So, the solution is -1 < x < 6

4. |x + 8.8| < 2.2: This absolute value inequality breaks down into two separate inequalities:

x + 8.8 > 2.2 or x + 8.8 < -2.2

1st part: x + 8.8 > 2.2 Subtract 8.8 from both sides to isolate x: x > 2.2 - 8.8 x > -6.6

2nd part: x + 8.8 < -2.2 Subtract 8.8 from both sides to isolate x: x < -2.2 - 8.8 x < -11

So, the solution is -11 < x < -6.6

5. |7.1 - x| > 8.2: This absolute value inequality breaks down into two separate inequalities:

7.1 - x > 8.2 or 7.1 - x < -8.2

1st part: 7.1 - x > 8.2 Subtract 7.1 from both sides to isolate x: -x > 8.2 - 7.1 -x > 1.1

Remember to flip the inequality sign when multiplying or dividing by a negative number:

x < -1.1

2nd part: 7.1 - x < -8.2 Subtract 7.1 from both sides to isolate x: -x < -8.2 - 7.1 -x < -15.3

Remember to flip the inequality sign:

x > 15.3

So, the solution is x < -1.1 or x > 15.3

6. |7.1 - x| > 8.2: This absolute value inequality breaks down into two separate inequalities:

7.1 - x > 8.2 or 7.1 - x < -8.2

1st part: 7.1 - x > 8.2 Subtract 7.1 from both sides to isolate x: -x > 8.2 - 7.1 -x > 1.1

Remember to flip the inequality sign when multiplying or dividing by a negative number:

x < -1.1

2nd part: 7.1 - x < -8.2 Subtract 7.1 from both sides to isolate x: -x < -8.2 - 7.1 -x < -15.3

Remember to flip the inequality sign:

x > 15.3

So, the solution is x < -1.1 or x > 15.3