Question

find the error a student solved the inequality shown below. the student made a mistake when solving the inequality.
$\frac{x}{2} < 4$
$\frac{x}{2} \div 2 < 4 \div 2$
$x < 2$
fix the student’s mistake and correct it by choosing the correct inequality signs, operations, and number.
$\frac{x}{2} < 4$
select choice < 4
select choice
$x <$ select choice

Explanation:

Step1: Analyze the student's step

The student had \(\frac{x}{2} < 4\) and then did \(\frac{x}{2}\div2 < 4\div2\). But to solve \(\frac{x}{2}<4\), we should multiply both sides by 2, not divide by 2.

Step2: Correct the operation

Multiply both sides of \(\frac{x}{2}<4\) by 2: \(\frac{x}{2}\times2 < 4\times2\), which simplifies to \(x < 8\). So the student's mistake was in the operation (used division by 2 instead of multiplication by 2) and the resulting number (got \(x < 2\) instead of \(x < 8\)).

Answer:

The student should multiply both sides by 2 (not divide by 2). The correct solution is \(x < 8\) (instead of \(x < 2\)). The error was in the operation (dividing by 2) and the resulting inequality. The correct inequality after solving \(\frac{x}{2}<4\) is \(x < 8\).