Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b – 8.1. Which student's first step was incorrect, and why?

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Here is the complete question:

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality

7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.

Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6.

Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.

Which student’s first step was incorrect, and why?

a. Amelia’s, because the variable term must be isolated on the left side

b. Luis’s, because he flipped the inequality sign when he subtracted

c. Shauna’s, because she did not apply the subtraction property of equality properly.

d. Clarence’s, because the terms he added together were not like terms.

The inequality given is:

7.2b + 6.5 > 4.8b – 8.1.

We are informed that Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

If Luis started by subtracting 4.8b from both sides, he should get:

7.2b + 6.5 > 4.8b – 8.1.

7.2b + 6.5 - 4.8b > 4.8b – 8.1 - 4.8b

2.4b + 6.5 > - 8.1

But looking critically, we would realise that what Luis got us different as the inequality sign has been changed from greater than to less than and this is incorrect.

The inequality sign can only be flipped in case whereby there's a division or multiplication of a negative number from both sides.

Therefore, Luis’s first step was incorrect because he flipped the inequality sign when he subtracted.