Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. find the error in the calculations below, if there is one: line (1): $-\frac{5x}{4} - \frac{7}{2} < -\frac{3}{8}$ line (2): $10x + 28 < -3$ line (3): $10x < -31$ line (4): $x < -\frac{31}{10}$ line (5): number line with an open circle at $-\frac{31}{10}$ and shading to the left \\(\circ\\) there is no error. \\(\circ\\) the error occurred from line (3) to line (4). \\(\circ\\) the error occurred from line (4) to line (5). \\(\circ\\) the error occurred from line (1) to line (2).

Explanation:

Step1: Analyze Line (1) to Line (2)

To eliminate fractions in Line (1): \(-\frac{5x}{4}-\frac{7}{2}<-\frac{3}{8}\), we multiply each term by the least common denominator (LCD) of 4, 2, and 8, which is 8.

• Multiply \(-\frac{5x}{4}\) by 8: \(8\times(-\frac{5x}{4})=-10x\)
• Multiply \(-\frac{7}{2}\) by 8: \(8\times(-\frac{7}{2})=-28\)
• Multiply \(-\frac{3}{8}\) by 8: \(8\times(-\frac{3}{8})=-3\)

So after multiplying by 8, the inequality should be \(-10x - 28 < - 3\), but Line (2) has \(10x + 28 < - 3\). The signs of the terms were incorrectly changed (the \(-10x\) became \(10x\) and \(-28\) became \(+28\)), so the error is from Line (1) to Line (2).

Answer:

The error occurred from line (1) to line (2).