11
Question The steps to solve three equations are shown below. Identify and correct any mistakes.
(a) 6x + 9 = 66
x + 9 = 11
x = 11 – 9
x = 2
(b) 14y + 24 = 36
7y + 12 = 18
7y = 6
y = \(\frac {6}{7}\)
(c) 4x – 5 = 9x + 8
4x = 9x + 8 – 5
4x = 9x + 3
4x – 9x = 3
-5x = 3
x = \(\frac {-5}{3}\)
(a) 6x + 9 = 66 → Error Variable terms should be on one side and constants on the other side before separating the coefficient from the variable. Correction 6x + 9 = 66 6x = 66 – 9 6x = 57 x = \(\frac {57}{6}\) x = \(\frac {19}{2}\) x = 9\(\frac {1}{2}\) (b) 14y + 24 = 36 7y + 12 = 18 [Dividing by 2 throughout] 7y = 6 y = \(\frac {6}{7}\) → No Error (c) 4x – 5 = 9x + 8 4x = 9x + 8 – 5 → Error 4x = 9x + 3 4x – 9x = 3 -5x = 3 x = \(\frac {-5}{3}\) → Error Correction 4x – 5 = 9x + 8 4x = 9x + 8 + 5 4x = 9x + 13 4x – 9x = 13 -5x = 13 x = \(\frac {-13}{5}\) x = -2\(\frac {3}{5}\)