Question

Frank tried to solve an equation step by step. \qquad\begin{aligned} -5&=5(d+4)\\\\ \\ -5&=5d+20&\green{\text{Step } 1}\\\\ \\ 15&=5d&\blue{\text{Step } 2}\\\\ \\ 3&=d&\purple{\text{Step } 3}\\\\ \end{aligned} −5 −5 15 3 ​ =5(d+4) =5d+20 =5d =d ​ Step 1 Step 2 Step 3 ​ Find Frank's mistake.

Answer 1

step 2

Explanation:

Answer 2

Frank incorrectly subtracted 20 in Step 2.

Explanation:

Frank's work is apparently ...

`\begin{aligned} -5&=5(d+4)\\ -5&=5d+20&\green{\text{Step } 1}\\15&=5d&\blue{\text{Step } 2}\\ 3&=d&\purple{\text{Step } 3}\end{aligned}`

Step 2 is apparently the step where Frank eliminates 20 from the right side of the equation. That is done by adding -20 to both sides. The error seems to be that Frank added -20 to the right side, but added +20 to the left side. The result of Step 2 should have been

-25 = 5d . . . . Step 2

-5 = d . . . . . . .Step 3

_____

Comment on Frank's solution

Sometimes students are told to "move the constant to the other side and change its sign." There is no rule of equality that supports that instruction for solving an equation.

Rather, the applicable rule is "do the same thing to both sides of the equation." When a constant is to be removed, that "same thing" is to "add the opposite of the constant to both sides of the equation." If you keep this rule in mind, it can help prevent sign mistakes of the kind that Frank made.