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?

Amelia’s, because the variable term must be isolated on the left side
Luis’s, because he flipped the inequality sign when he subtracted
Shauna’s, because she did not apply the subtraction property of equality properly
Clarence’s, because the terms he added together were not like terms

Answer 1

Luis made a mistake by flipping the inequality sign when subtracting 4.8b from both sides. The inequality sign is only flipped when the expression id multiplies of divided by a negative value.

Explanation:

7.2b + 6.5 > 4.8b – 8.1

Amelia started by subtracting 7.2b from both sides

7.2b + 6.5 > 4.8b – 8.1

6.5 > 4.8b – 8.1 - 7.2b

6.5 > -2.4b – 8.1

Amelia got 6.5 > –2.4b – 8.1., which is Correct

Luis started by subtracting 4.8b from both sides

7.2b + 6.5 > 4.8b – 8.1

2.4b + 6.5 > - 8.1

Luis got 2.4b + 6.5 < – 8.1., which is Incorrect

Luis flipped the inequality sign when subtracting 4.8b from both sides. The inequality sign is only flipped when the expression id multiplies of divided by a negative value.

Shauna started by subtracting 6.5 from both sides

7.2b + 6.5 > 4.8b – 8.1

7.2b > 4.8b – 14.6

Shauna got 7.2b > 4.8b – 14.6, which is Correct

Clarence started by adding 8.1 to both sides

7.2b + 6.5 > 4.8b – 8.1

7.2b + 14.6 > 4.8b

Clarence got 7.2b + 14.6 > 4.8b., which is Correct