MATHEMATICS

JAMB 2014 - Question 18

Mathematics 2014 JAMB Past Questions - Question 18: Evaluate the inequality x/2+3/4

Evaluate the inequality x/2+3/4<=5x/6-7/12
A:
B:
C:
D:
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Correct Answer

B

Explanation

To evaluate the inequality (x/2) + (3/4) ≤ (5x/6) - (7/12), we can follow these steps:Step 1: Simplify both sides of the inequality by finding a common denominator.The common denominator for 2, 4, 6, and 12 is 12. Multiplying each term by the appropriate factor to obtain the common denominator, we have:(6x/12) + (9/12) ≤ (10x/12) - (7/12)Simplifying further, we get:(6x + 9)/12 ≤ (10x - 7)/12Step 2: Multiply both sides of the inequality by 12 to eliminate the denominators:12 * [(6x + 9)/12] ≤ 12 * [(10x - 7)/12]Simplifying, we have:6x + 9 ≤ 10x - 7Step 3: Rearrange the terms to isolate the variable on one side of the inequality:6x - 10x ≤ -7 - 9-4x ≤ -16Step 4: Divide both sides of the inequality by -4. Since we are dividing by a negative number, the direction of the inequality sign will be reversed:x ≥ (-16)/(-4)x ≥ 4Therefore, the solution to the inequality (x/2) + (3/4) ≤ (5x/6) - (7/12) is x ≥ 4.