Question on: JAMB Mathematics - 2024
Find the values of x for which
\(\frac{x+2}{4} - \frac{2x-3}{3} < 4\)
A
x < 8
B
x > -6
C
x < 4
D
x > -3
Ask EduPadi AI for a detailed answer
Correct Option: B
We are tasked with solving the inequality:
\( \frac{x+2}{4} - \frac{2x-3}{3} < 4 \)
First, we multiply both sides of the inequality by 12 (the least common multiple of 4 and 3) to eliminate the fractions:
\( 12 \times \left( \frac{x+2}{4} - \frac{2x-3}{3} \right) < 12 \times 4 \)
Which simplifies to:
\( 3(x+2) - 4(2x-3) < 48 \)
Now, distribute and simplify:
\( 3x + 6 - 8x + 12 < 48 \)
\( -5x + 18 < 48 \)
Subtract 18 from both sides:
\( -5x < 30 \)
Divide both sides by -5 (and reverse the inequality sign):
\( x > -6 \)
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