Find the number of integers that satisfy the compound inequality -3 < 2x + 1 \le 9. — JAMB UTME

Find the number of integers that satisfy the compound inequality $-3 < 2x + 1 \le 9$ .

Answer: 6

The number of integer solutions satisfying the inequality is 6.

Subtracting 1 across

-3 < 2x + 1 \le 9

gives

-4 < 2x \le 8

. Dividing by 2 yields

-2 < x \le 4

. The integers in this interval are

-1, 0, 1, 2, 3,

and

4

, giving a total of 6 integer solutions.

Subtract 1 from all parts of the compound inequality.

-4 < 2x \le 8

Isolate the variable term

2x

in the middle.

Divide all parts by 2.

-2 < x \le 4

Solve for

x

by undoing the coefficient of 2.

Identify the set of integer solutions within the interval

(-2, 4]

x \in \{-1, 0, 1, 2, 3, 4\}

The endpoint

-2

is excluded due to the strict inequality (

<

), while the endpoint

4

is included due to the inclusive inequality (

\\le

Count the elements in the solution set.

There are 6 distinct integer values in the set.

Solving compound linear inequalities and identifying integer solution sets.

Question