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

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

Step-by-step 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