Question

Bryce tried to solve an equation step by step. \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}

Answer 1

Bryce is wrong in step 1 because he did not distribute 3 over 5/3

Step-by-step explanation

Given the steps taken by bryce as shown, we are to find where he made an error

`\qquad\begin{aligned} \frac83&=3\left(c+\frac53\right)\\\\ \\ \frac83&=3c+\frac53&\green{\text{Step } 1}\\\\ \\ 1&=3c&\blue{\text{Step } 2}\\\\ \\ \frac13&=c&\purple{\text{Step } 3}\\\\ \end{aligned}`

Given the expression;

`\frac83&=3\left(c+\frac53\right)\\\\ \\`

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