Solve the inequality 2x + 3 > 5x + 8

Analysis

The goal is to solve for $x$ in the linear inequality $2x + 3 > 5x + 8$. Solving an inequality is very similar to solving an equation, but you must be careful when multiplying or dividing by a negative number, as that flips the inequality sign.

Concept

To solve this, we need to group the terms containing $x$ on one side and the constant terms on the other side.

Step-by-Step Solution

Step 1: Group the terms Subtract $5x$ from both sides of the inequality to bring all $x$ terms to the left: $2x - 5x + 3 > 8$ $-3x + 3 > 8$

Step 2: Isolate the $x$ term Subtract $3$ from both sides: $-3x > 8 - 3$ $-3x > 5$

Step 3: Solve for $x$ Divide both sides by $-3$. Important Rule: Whenever you divide or multiply an inequality by a negative number, you must reverse the inequality sign ($>$ becomes $<$).

$x < \frac{5}{-3}$

Step 4: Simplify the fraction $x < -\frac{5}{3}$

Converting the improper fraction to a mixed fraction: $5 \div 3 = 1$ remainder $2$ So, $x < -1\frac{2}{3}$

Conclusion

Comparing our result ($x < -1\frac{2}{3}$) with the given options, it matches option C.

Exam Tip

Always double-check your inequality sign when dealing with negative coefficients. A common mistake in JAMB is forgetting to flip the sign when dividing by a negative number, which would lead you to choose the wrong direction (like option B).