Question

The setA={ x : |2x+3|<7 } is equal to the set : *
1 point
D= { x: 0<x+5<7 }
B= { x: -3<x<7 }
E= { x: -7<x<7 }
C= { x: -13<2x<4 }​

Answer 1

Answer :

D = { x : 0 < x + 5 < 7 }

Note :

• If |x| = a , then x = ± a .

• If |x| < a , then -a < x < a .

[ x € (-a,a) ]

• If x| > a , then x < -a or x > a .

[ x € (-∞,-a)U(a,∞) ]

Solution :

Given :

A = { x : |2x + 3| < 7 }

Let's find the elements of set A .

We know that ,

If |x| < a , then -a < x < a .

Thus ,

If |2x + 3| < 7 , then -7 < 2x + 3 < 7 .

→ -7 < 2x + 3 < 7

→ -7 - 3 < 2x + 3 - 3 < 7 - 3

→ -10 < 2x < 4

→ -10/2 < 2x/2 < 4/2

→ -5 < x < 2

→ x € (-5,2)

Hence , A = (-5,2)

ie. A = { x : -5 < x < 2 }

But , -5 < x < 2 can be written as ;

→ -5 < x < 2

→ -5 + 5 < x + 5 < 2 + 5

→ 0 < x + 5 < 7

Hence ,

Correct answer is :

D = { x : 0 < x + 5 < 7 }