Question

find the error in the calculations below, if there is one: line (1): -5 ≤ 2x + 7 < 9 line (2): -12 ≤ 2x < 2 line (3): -6 ≤ x < 1 line (4): a number - line with -6 filled - in and 1 open - circle the error occurred from line (2) to line (3). the error occurred from line (1) to line (2). the error occurred from line (3) to line (4). there are no errors.

Explanation:

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

Subtract 7 from all parts of -5 ≤ 2x + 7 < 9. We get -5 - 7 ≤ 2x+7 - 7 < 9 - 7, which simplifies to -12 ≤ 2x < 2. This step is correct.

Step2: Analyze Line (2) to Line (3)

Divide all parts of -12 ≤ 2x < 2 by 2. We have $\frac{-12}{2}\leq\frac{2x}{2}<\frac{2}{2}$, resulting in -6 ≤ x < 1. This step is correct.

Step3: Analyze Line (3) to Line (4)

The inequality -6 ≤ x < 1 is correctly represented on the number - line with a closed - circle at -6 (because x can equal -6) and an open - circle at 1 (because x cannot equal 1). This step is correct.

Answer:

There are no errors.