Answer:
Bryce is wrong in step 1 because he did not distribute 3 over 5/3
Explanation
Given the steps taken by bryce as shown, we are to find where he made an error
[tex]\qquad\begin{aligned} \dfrac83&=3\left(c+\dfrac53\right)\\\\ \\ \dfrac83&=3c+\dfrac53&\green{\text{Step } 1}\\\\ \\ 1&=3c&\blue{\text{Step } 2}\\\\ \\ \dfrac13&=c&\purple{\text{Step } 3}\\\\ \end{aligned}[/tex]
Given the expression;
[tex]\dfrac83&=3\left(c+\dfrac53\right)\\\\ \\[/tex]
Step 1:Expand the bracket using the distributive law;
8/3 = 3c + 3(5/3)
Simplify
8/3 = 3c + 15/3
Step 2: Subtract 15/3 from both sides
8/3 - 15/3 = 3c+15/3-15/3
(8-15)/3 = 3c
-7/3 = 3c
Step 3: Multiply both sides by 1/3
-7/3 * 1/3 = 3c * 1/3
-7/9 = c
Swap
c = -7/9
From the calculation, we can see that Bryce is wrong in step 1 because he did not distribute 3 over 5/3 thereby making his solution incorrect
