Determine the smallest integer value of x that satisfies the compound inequality 3 < 2x - … — JAMB UTME

Determine the smallest integer value of $x$ that satisfies the compound inequality $3 < 2x - 5 \le 11$ .

Answer: 5

The smallest integer value of

x

that satisfies the inequality is 5.

Adding 5 across the compound inequality

3 < 2x - 5 \le 11

gives

8 < 2x \le 16

. Dividing by 2 yields

4 < x \le 8

. The integer values satisfying this range are 5, 6, 7, and 8. Therefore, the smallest integer solution is 5.

Add 5 to all parts of the compound inequality

8 < 2x <= 16

Isolates the variable term in the middle segment.

Divide all parts of the compound inequality by 2

4 < x <= 8

Solves for x without changing inequality signs since 2 is positive.

Identify integer solutions within the range (4, 8]

x in {5, 6, 7, 8}

Since the inequality at 4 is strict (<), 4 is excluded, but 8 is included (<=).

Find the minimum integer value in the solution set

5 is the smallest integer strictly greater than 4.

Solving Compound Linear Inequalities

Question