Ghoul Sides
x + 4 = 2x - 7
Answer: x = 11
4 - 2q = 10 + q
Answer: q = -2
7 = (x / 5) + 2
Answer: x = 25
-3x ≤ 21
Answer: x ≥ -7
From x + 4 = 2x - 7 a student writes 4 - 4 = 2x - (7 - 4).
Answer: Must subtract 4 from the entire RHS → 2x - 7 - 4 = 2x - 11
2y - 5 = 7 - y
Answer: y = 4
3(x + 2) = 2x - 5
Answer: x = -11
(x - 2) / 4 = (3x + 1) / 2
Answer: x = -4/5
-2(x - 5) ≥ 8
Answer: x ≤ 1
From -3x ≤ 12 a student divides by 3 to get x ≤ 4.
Answer: Divided by a negative → flip sign → x ≥ -4
5 - p = 2p + 16
Answer: p = -11/3
5(2 - x) = 3x + 10
Answer: x = 0
(x / 3) + 4 = (2x - 1) / 5
Answer: x = 63
-(3/4)x > 6
Answer: x < -8
Clearing (x - 2)/4 = (3x + 1)/2, a student multiplies by 4 and writes x - 2 = 3x + 1.
Answer: Must multiply both sides by 4 → x - 2 = 2(3x + 1)
7 - 3x = x + 15
Answer: x = -2
-2(x - 7) + 3 = x - 8
Answer: x = 25/3
(2/3)x + 5 = (1/6)x - 7
Answer: x = -24
2(x - 7) ≤ -x + 5
Answer: x ≤ 19/3
Distributing -3(2 - x), a student writes -6 - 3x.
Answer: Sign error → correct distribution is -6 + 3x
3(x - 2) + 5 = 2x - 1
Answer: x = 0
6(x - 1) - 2 = 4x + 10
Answer: x = 9
(x / 2) + (x / 3) = 10
Answer: x = 12
-(1/2)x + 7 ≥ 3
Answer: x ≤ 8
Solving 5 - p = 2p + 16, a student ends with p = 11/3.
Answer: Sign error → correct p = -11/3