Question

Which compound equalities have x = 2 as a solution? Check all that apply

Answer 1

Answer:

$(a)\ 4 < 5x - 1 < 10$

$(b)\ 4 < 5x - 3 < 10$

$(d)\ 4 < 2x + 1 < 10$

$(e)\ 4 < 2x + 3 < 10$

Step-by-step explanation:

Required

Whose solution is $x = 2$

$(a)\ 4 < 5x - 1 < 10$

Add 1 to both parts

$4 +1< 5x < 10+1$

$5< 5x < 11$

Divide through by 5

$1< x$

Substitute 2 for x

$1< 2$ --- this is true

$(b)\ 4 < 5x - 3 < 10$

Add 3 to both parts

$4 +3< 5x < 10+3$

$7< 5x < 13$

Divide by 5

$1.4< x < 2.6$

Substitute 2 for x

$1.4 < 2 < 2.6$ --- this is true

$(c)\ 4 < 5x - 7 < 10$

Add 7 to both parts

$4 +7< 5x < 10+7$

$12< 5x < 17$

Divide by 5

$2.4< x < 3.4$

Substitute 2 for x

$2.4< 2 < 3.4$ --- this is false because 2.4 > 2

$(d)\ 4 < 2x + 1 < 10$

Subtract 1 from all parts

$4 - 1$

$3$

Divide by 2

$1.5 < x < 4.5$

Substitute 2 for x

$1.5 < 2 < 4.5$ --- this is true

$(e)\ 4 < 2x + 3 < 10$

Subtract 3 from all parts

$4 -3< 2x < 10-3$

$1 < 2x < 7$

Divide by 2

$0.5 < x < 3.5$

Substitute 2 for x

$0.5 < 2 < 3.5$  ----- this is true

$(f)\ 4 < 2x + 6 < 10$

Subtract 6 from all parts

$4 -6< 2x< 10-6$

$-2< 2x< 4$

Divide by 2

$-1< x< 2$

Substitute 2 for x

$-1< 2< 2$ --- this is false because 2 = 2; not 2 < 2