Question

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

Explanation:

Here, the given inequality,

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

By the subtraction property of inequality,

The answer will not changez

Thus, her first step is not incorrect.

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

He flipped the sign of inequality when he applied subtraction property of inequality which is wrong,

⇒ His first step is incorrect.

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

By the subtraction property of inequality,

The answer will not change,

Thus, her first step is not incorrect.

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

By the Additive property of inequality,

The answer will not change,

Thus, his first step is not incorrect.

Hence, only Luis's first step was incorrect.

Answer 2

• Clarence's step is incorrect:

Whenever an equation is simplified, only like terms can be added to each other. If unlike terms will be added, answer will always be wrong. This mean terms with same variables are added into each other and constants are added into each other.

• Amelia’s step is correct

• Luis’s step is correct
• Shauna’s step is correct