Answer :
Let's simplify the expression step-by-step to identify where Clara made an error.
We start with the expression: [tex]\((8b - 4r) - (2b - r)\)[/tex].
1. Distribute the negative sign:
- The negative sign in front of the second parenthesis changes the sign of each term inside it.
- So, [tex]\((2b - r)\)[/tex] becomes [tex]\(-2b + r\)[/tex].
2. Rewrite the expression:
- After distributing the negative sign, the expression becomes:
[tex]\[
8b - 4r - 2b + r
\][/tex]
3. Combine like terms:
- For [tex]\(b\)[/tex] terms: [tex]\(8b - 2b\)[/tex] gives [tex]\(6b\)[/tex].
- For [tex]\(r\)[/tex] terms: [tex]\(-4r + r\)[/tex] gives [tex]\(-3r\)[/tex].
4. Write the simplified expression:
- The correctly simplified expression is [tex]\(6b - 3r\)[/tex].
Clara incorrectly combined the [tex]\(r\)[/tex] coefficients. The correct simplified expression should be [tex]\(6b - 3r\)[/tex], not [tex]\(6b - 5r\)[/tex]. Hence, the error was in combining the [tex]\(r\)[/tex] coefficients.
We start with the expression: [tex]\((8b - 4r) - (2b - r)\)[/tex].
1. Distribute the negative sign:
- The negative sign in front of the second parenthesis changes the sign of each term inside it.
- So, [tex]\((2b - r)\)[/tex] becomes [tex]\(-2b + r\)[/tex].
2. Rewrite the expression:
- After distributing the negative sign, the expression becomes:
[tex]\[
8b - 4r - 2b + r
\][/tex]
3. Combine like terms:
- For [tex]\(b\)[/tex] terms: [tex]\(8b - 2b\)[/tex] gives [tex]\(6b\)[/tex].
- For [tex]\(r\)[/tex] terms: [tex]\(-4r + r\)[/tex] gives [tex]\(-3r\)[/tex].
4. Write the simplified expression:
- The correctly simplified expression is [tex]\(6b - 3r\)[/tex].
Clara incorrectly combined the [tex]\(r\)[/tex] coefficients. The correct simplified expression should be [tex]\(6b - 3r\)[/tex], not [tex]\(6b - 5r\)[/tex]. Hence, the error was in combining the [tex]\(r\)[/tex] coefficients.
