Answer :
To help Clara understand her mistake in simplifying the expression [tex]\((8 - 4r) - (28 - r)\)[/tex], let's go through the steps to simplify it correctly.
1. Remove the Parentheses:
Begin by distributing the negative sign across the second set of parentheses:
- Apply the negative sign to each term inside the parentheses:
[tex]\[
(8 - 4r) - (28 - r) = 8 - 4r - 28 + r
\][/tex]
2. Combine Like Terms:
Next, gather and combine the like terms from the expression:
- Constant Terms: Combine the numbers 8 and -28:
[tex]\[
8 - 28 = -20
\][/tex]
- 'r' Terms: Combine the terms with 'r', which are -4r and +r:
[tex]\[
-4r + r = -3r
\][/tex]
3. Final Simplified Expression:
Putting the combined terms together gives us:
[tex]\[
-20 - 3r
\][/tex]
Clara's original result was [tex]\(6b - 5r\)[/tex], which indicates that she made a mistake. It seems she incorrectly combined the terms with 'r'. The correctly simplified expression is [tex]\(-20 - 3r\)[/tex].
So, the error Clara made was in combining the coefficients of the 'r' terms. The correctly simplified expression is [tex]\(-20 - 3r\)[/tex].
1. Remove the Parentheses:
Begin by distributing the negative sign across the second set of parentheses:
- Apply the negative sign to each term inside the parentheses:
[tex]\[
(8 - 4r) - (28 - r) = 8 - 4r - 28 + r
\][/tex]
2. Combine Like Terms:
Next, gather and combine the like terms from the expression:
- Constant Terms: Combine the numbers 8 and -28:
[tex]\[
8 - 28 = -20
\][/tex]
- 'r' Terms: Combine the terms with 'r', which are -4r and +r:
[tex]\[
-4r + r = -3r
\][/tex]
3. Final Simplified Expression:
Putting the combined terms together gives us:
[tex]\[
-20 - 3r
\][/tex]
Clara's original result was [tex]\(6b - 5r\)[/tex], which indicates that she made a mistake. It seems she incorrectly combined the terms with 'r'. The correctly simplified expression is [tex]\(-20 - 3r\)[/tex].
So, the error Clara made was in combining the coefficients of the 'r' terms. The correctly simplified expression is [tex]\(-20 - 3r\)[/tex].
