Question

12What mistake did the student make when solvingtheir two-step equation?(a)b) If correctly solved what should the value of be?

Answer 1

Given the equation:

$\frac{x}{6}+3=-18$

(a) You can identify that the student applied the Subtraction Property of Equality by subtraction 3 from both sides of the equation:

$\frac{x}{6}+3-(3)=-18-(3)$

However, the student made a mistake when adding the numbers on the right side.

Since you have two numbers with the same sign on the right side of the equation, you must add them, not subtract them and use the same sign in the result. Then, the steps to add them are:

- Add their Absolute values (their values without the negative sign).

- Write the sum with the negative sign.

Then:

$\frac{x}{6}=-21$

(b) The correct procedure is:

1. Apply the Subtraction Property of Equality by subtracting 3 from both sides (as you did in the previous part):

$\begin{gathered} \frac{x}{6}+3-(3)=-18-(3) \\ \\ \frac{x}{6}=-21 \end{gathered}$

2. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 6:

$\begin{gathered} (6)(\frac{x}{6})=(-21)(6) \\ \\ x=-126 \end{gathered}$

Hence, the answers are:

(a) The student made a mistake by adding the numbers -18 and -3:

$-18-3=-15\text{ (False)}$

(b) The value of "x" should be:

$x=-126$