Question

Moira solved a problem on the board. What error did Moira make and how can she correct it?

12.25x + 10 = 54 – 10.25x
12.25x + 10 – 10 = 54 – 10.25x – 10
12.25x = 44 – 10.25x
12.25x – 10.25x = 44 – 10.25x + 10.25x
2x = 44
x = 22

Answer 1

Moira's error was not correctly combining like terms; she should have combined the x terms by adding them together and then divided by the sum of their coefficients to find that x = 1.9556.

Step-by-step explanation:

Moira made an error in combining like terms and solving the equation correctly. The correct steps to solve the equation 12.25x + 10 = 54 - 10.25x are:

Bring like terms involving x to the same side: 12.25x + 10.25x = 54 - 10.

Add the coefficients of x: (12.25 + 10.25)x = 44.

Simplify the equation: 22.5x = 44.

Divide both sides by 22.5 to isolate x: x = 44 / 22.5.

Calculate the value of x: x = 1.9556 (rounded to four decimal places).

Therefore, the correct solution is x = 1.9556, not x = 22 as Moira originally concluded.