Question

Is the inequality always, sometimes, or never true? 13. 3(2x + 1) > 5x − (2 − x)​14. 2(x − 1) ≥ x + 7 15. 7x + 2 ≤ 2(2x − 4) + 3x​16. 5(x − 3) < 2(x − 9)

Answer 1

13. 3(2x + 1) > 5x - (2 - x)
6x + 3 > 5x - 2 + x
6x + 3 > 6x - 2
6x - 6x > -2 - 3
0 > -5.....ALWAYS TRUE

14. 2(x - 1) > = x + 7
2x - 2 > = x + 7
2x - x > = 7 + 2
x > = 9.....SOMETIMES TRUE

15. 7x + 2 < = 2(2x - 4)
7x + 2 < = 4x - 8
7x - 4x < = -8 - 2
3x < = - 10
x < = -10/3....SOMETIMES TRUE

16. 5(x - 3) < 2(x - 9)
5x - 15 < 2x - 18
5x - 2x < -18 + 15
3x < -3
x < -3/3
x < -1.....SOMETIMES TRUE

Answer 2

13. 3(2x + 1) > 5x - (2 - x)

6x + 3 > 5x - 2 + x

6x + 3 > 6x - 2

6x - 6x > -2 - 3

0 > -5..... always true

14. 2(x - 1) > = x + 7

2x - 2 > = x + 7

2x - x > = 7 + 2

x > = 9....sometimes true

15. 7x + 2 < = 2(2x - 4)

7x + 2 < = 4x - 8

7x - 4x < = -8 - 2

3x < = - 10

x < = -10/3....sometimes true

16. 5(x - 3) < 2(x - 9)

5x - 15 < 2x - 18

5x - 2x < -18 + 15

3x < -3

x < -3/3

x < -1.....sometimes true