Question

Moira solved a problem on the board. What error did Moira make and how can she correct it? 12x + 10 = 54 – 10x 12x + 10 – 10 = 54 – 10x – 10 12x = 44 – 10x 12x – 10x = 44 – 10x + 10x 2x = 44 x = 22

Answer 1

Answer:

Moira didn't add $10x$ to both sides of the equation in the fourth step she applied (this is: $12x - 10x = 44 - 10x + 10x$).

She can correct it applying the Addition property of equality and add $10x$ to both sides of the equation then she must apply the Division property of equality  (See the procedure below).

Step-by-step explanation:

Given the equation:

$12x + 10 = 54 - 10x$

The steps to solve it are:

1. According to the Subtraction property of equality, you we can subtract 10 from both sides of the equation:

$12x + 10-10 = 54 - 10x-10\\\\12x = 44 - 10x$

2. Based on the Addition property of equality, you we can add $10x$ to both sides of the equation:

$12x +10x= 44 - 10x+10x\\\\22x=44$

3. Finally, applying the Division property of equality, we must divide both sidesby 22:

$\frac{22x}{2}=\frac{44}{22}\\\\x=2$

Therefore, she made an error in fourth step she applied:

$12x - 10x = 44 - 10x + 10x$  

Because she didn't add $10x$ to both sides of the equation.

She can correct it applying the Addition property of equality and add $10x$ to both sides of the equation and then she must apply the Division property of equality  (As you can observe in the procedure shown above).