Find the largest integer value of x that satisfies the linear inequality \frac{2x - 5}{3} … — JAMB UTME

Find the largest integer value of $x$ that satisfies the linear inequality $\frac{2x - 5}{3} \le \frac{x + 1}{4}$ .

Answer: 4

Answer

The largest integer value of

x

satisfying the inequality is 4.

Multiplying the entire inequality by 12 yields 4(2x - 5) <= 3(x + 1). Expanding both sides produces 8x - 20 <= 3x + 3. Subtracting 3x and adding 20 gives 5x <= 23, which simplifies to x <= 4.6. The largest integer less than or equal to 4.6 is 4.

Step-by-Step Solution

Clear the denominators by multiplying both sides by 12.

4(2x - 5) \le 3(x + 1)

Multiplying by a positive number preserves the inequality direction while clearing fractions.

Expand both sides of the inequality using the distributive property.

8x - 20 \le 3x + 3

Multiply 4 through (2x - 5) and 3 through (x + 1).

Isolate the variable terms on one side and constant terms on the other.

5x \le 23 \implies x \le 4.6

Subtract 3x from both sides and add 20 to both sides, then divide by 5.

Determine the maximum integer value satisfying the inequality boundary.

Since x must be less than or equal to 4.6, the greatest whole integer satisfying this condition is 4.

Key Concept

Solving linear inequalities with fractions and finding integer bounds

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