Question

Solve the compound inequality-1<4m+7<11

Answer 1

Combing both the inequalities of m , we get -3/2 < m < 1

Explanation:

Here, the given expression is 1 < 4 m + 7 < 11.

Considering the left part of the equation we get

1 < 4 m + 7

or, 1 -7 < 4 m + 7 - 7

or, -6 < 4 m

or, m > -6/4

⇒ m > -3/2

Similarly, considering the right part of the equation:

4 m + 7 < 11

or, 4 m + 7 - 7 < 11 - 7

or, 4 m < 4

or, m< 4/4 = 1

⇒ m < 1

Hence, combing both the inequalities of m ,

m > -3/2

m < 1

⇒ -3/2 < m < 1