Question

Which compound equalities have x = 2 as a solution? Check all that apply. 4 < 5x – 1 < 10 4 < 5x – 3 < 10 4 < 5x – 7 < 10 4 < 2x + 1 < 10 4 < 2x + 3 < 10 4 < 2x + 6 < 10

Answer 1

Answer:

4 < 5x – 1 < 10  

4 < 5x – 3 < 10  

4 < 2x + 1 < 10  

4 < 2x + 3 < 10

Answer 2

For this case, the first thing to do is substitute the value of x = 2 in each of the compound inequations and verify that the inequations are met.
 We have then:

 For 4 <5x - 1 <10:
 4 <5 (2) - 1 <10
 4 <10 - 1 <10
 4 <9 <10
 The inequality is fulfilled.

 For 4 <5x - 3 <10:
 4 <5 (2) - 3 <10
 4 <10 - 3 <10
 4 <7 <10
 The inequality is fulfilled.

 For 4 <5x - 7 <10:
 4 <5 (2) - 7 <10
 4 <10 - 7 <10
 4 <3 <10
 The inequality is not fulfilled.

 For 4 <2x + 1 <10
 4 <2 (2) + 1 <10
 4 <4 + 1 <10
 4 <5 <10
 The inequality is fulfilled.

 For 4 <2x + 3 <10:
 4 <2 (2) + 3 <10
 4 <4 + 3 <10
 4 <7 <10
 The inequality is fulfilled.

 For 4 <2x + 6 <10
 4 <2 (2) + 6 <10
 4 <4 + 6 <10
 4 <10 <10
 The inequality is not fulfilled.