Answer:
[tex](a)\ 4 < 5x - 1 < 10[/tex]
[tex](b)\ 4 < 5x - 3 < 10[/tex]
[tex](d)\ 4 < 2x + 1 < 10[/tex]
[tex](e)\ 4 < 2x + 3 < 10[/tex]
Step-by-step explanation:
Required
Whose solution is [tex]x = 2[/tex]
[tex](a)\ 4 < 5x - 1 < 10[/tex]
Add 1 to both parts
[tex]4 +1< 5x < 10+1[/tex]
[tex]5< 5x < 11[/tex]
Divide through by 5
[tex]1< x<2.2[/tex]
Substitute 2 for x
[tex]1< 2<2.2[/tex] --- this is true
[tex](b)\ 4 < 5x - 3 < 10[/tex]
Add 3 to both parts
[tex]4 +3< 5x < 10+3[/tex]
[tex]7< 5x < 13[/tex]
Divide by 5
[tex]1.4< x < 2.6[/tex]
Substitute 2 for x
[tex]1.4 < 2 < 2.6[/tex] --- this is true
[tex](c)\ 4 < 5x - 7 < 10[/tex]
Add 7 to both parts
[tex]4 +7< 5x < 10+7[/tex]
[tex]12< 5x < 17[/tex]
Divide by 5
[tex]2.4< x < 3.4[/tex]
Substitute 2 for x
[tex]2.4< 2 < 3.4[/tex] --- this is false because 2.4 > 2
[tex](d)\ 4 < 2x + 1 < 10[/tex]
Subtract 1 from all parts
[tex]4 - 1 <2x<10-1[/tex]
[tex]3 <2x<9\\[/tex]
Divide by 2
[tex]1.5 < x < 4.5[/tex]
Substitute 2 for x
[tex]1.5 < 2 < 4.5[/tex] --- this is true
[tex](e)\ 4 < 2x + 3 < 10[/tex]
Subtract 3 from all parts
[tex]4 -3< 2x < 10-3[/tex]
[tex]1 < 2x < 7[/tex]
Divide by 2
[tex]0.5 < x < 3.5[/tex]
Substitute 2 for x
[tex]0.5 < 2 < 3.5[/tex] ----- this is true
[tex](f)\ 4 < 2x + 6 < 10[/tex]
Subtract 6 from all parts
[tex]4 -6< 2x< 10-6[/tex]
[tex]-2< 2x< 4[/tex]
Divide by 2
[tex]-1< x< 2[/tex]
Substitute 2 for x
[tex]-1< 2< 2[/tex] --- this is false because 2 = 2; not 2 < 2
