\hspace{0.8cm} + 8 = 22
Worked Solution & Answer
22 - 8 = 14 B1
Answer: 14
Solving one step equations — Notes & Worked Examples Show / Hide
Explanation:
Solving an equation means finding the value of the unknown letter that makes both sides equal. Think of the equation as a balanced scale: whatever operation you do to one side, you must do the exact same operation to the other side.
To isolate the letter in a one-step equation, apply the inverse (opposite) operation: undo + a by subtracting a, undo − a by adding a, undo × a by dividing by a, and undo ÷ a (a fraction xa) by multiplying by a.
Example 1: Solve:
(a) x + 9 = 23 (b) y − 7 = −3
Solution:
(a) Inverse of + 9 is − 9 on both sides:
• x = 23 − 9 → x = 14
(b) Inverse of − 7 is + 7 on both sides:
• y = −3 + 7 → y = 4
Example 2: Solve:
(a) 6m = 42 (b) w5 = 8
Solution:
(a) 6m means 6 × m, so divide both sides by 6:
• m = 42 ÷ 6 → m = 7
(b) w5 means w ÷ 5, so multiply both sides by 5:
• w = 8 × 5 → w = 40
\hspace{0.8cm} + 12 = 24
Worked Solution & Answer
24 - 12 = 12 B1
Answer: 12
Solve the following linear equations.
(a) Solve 12 - e = 0 [1 mark]
e =
(b) Solve 7f = 0 [1 mark]
f =
Worked Solution & Answer
(a)
12 - e = 0 ⇒ e = 12 B1
Answer (a): e = 12
(b)
7f = 0 ⇒ f = 0 B1
Answer (b): f = 0
(a) Solve 7x = 56
5 (b) Solve 25 - y = 18
5 (b) Solve 25 - y = 18
(a) Solve 7x = 56 [1 mark]
x =
(b) Solve 25 - y = 18 [1 mark]
y =
Worked Solution & Answer
(a)
x = 56 ÷ 7 = 8 B1
Answer (a): x = 8
(b)
y = 25 - 18 = 7 B1
Answer (b): y = 7
Solve.
(a) x3 = 6 [1 mark]
x =
(b) 2x = -14 [1 mark]
x =
Worked Solution & Answer
(a)
x = 6 × 3 = 18. B1
Answer (a): x = 18
(b)
x = −14 ÷ 2 = −7. B1
Answer (b): x = -7
Solve.
(a) x4 = 8 [1 mark]
x =
(b) 8 - x = -2 [1 mark]
x =
Worked Solution & Answer
(a)
x = 8 × 4 = 32. B1
Answer (a): x = 32
(b)
x = 8 − (−2) = 10. B1
Answer (b): x = 10
(a) Solve 5x = 15
1 (b) Solve y + 7 = 50
1 (c) Solve c4 = 8
1 (b) Solve y + 7 = 50
1 (c) Solve c4 = 8
(a) Solve 5x = 15 [1 mark]
x =
(b) Solve y + 7 = 50 [1 mark]
y =
(c) Solve c4 = 8 [1 mark]
c =
Worked Solution & Answer
(a)
x = 15 ÷ 5 = 3 B1
Answer (a): x = 3
(b)
y = 50 - 7 = 43 B1
Answer (b): y = 43
(c)
c = 8 × 4 = 32 B1
Answer (c): c = 32
(a) Solve t + t + t = 12 (1) (b) Solve x – 2 = 6 (1) (c) Solve 6w + 2 = 20 (2)
(a) Solve t + t + t = 12 [1 mark]
t =
(b) Solve x - 2 = 6 [1 mark]
x =
(c) Solve 6w + 2 = 20 [2 marks]
w =
Worked Solution & Answer
(a)
3t = 12 ⇒ t = 4 B1
Answer (a): t = 4
(b)
x = 6 + 2 = 8 B1
Answer (b): x = 8
(c)
6w = 18 M1
⇒ w = 3 A1
⇒ w = 3 A1
Answer (c): w = 3
(a) Solve 5x = 30 [1 mark]
3 (b) Solve -2 + y = 10 [1 mark]
3 (c) Simplify fully 20w / 4w [2 marks]
3 (b) Solve -2 + y = 10 [1 mark]
3 (c) Simplify fully 20w / 4w [2 marks]
(a) Solve 5x = 30 [1 mark]
x =
(b) Solve -2 + y = 10 [1 mark]
y =
(c) Simplify fully 20w4w [2 marks]
Answer
Worked Solution & Answer
(a)
x = 30 ÷ 5 = 6 B1
Answer (a): x = 6
(b)
y = 10 + 2 = 12 B1
Answer (b): y = 12
(c)
20w4w = 204 = 5 M1 A1
Answer (c): Answer 5
(a) Solve 5x = 30 (1) (b) Solve y – 7 = 12 (1) (c) Simplify h + h + h + h + h (1) (d) Simplify 5a + 7f – 2a + 4f (2)
(a) Solve 5x = 30 [1 mark]
x =
(b) Solve y - 7 = 12 [1 mark]
y =
(c) Simplify h + h + h + h + h [1 mark]
(d) Simplify 5a + 7f - 2a + 4f [2 marks]
Worked Solution & Answer
(a)
x = 30 ÷ 5 = 6 B1
Answer (a): x = 6
(b)
y = 12 + 7 = 19 B1
Answer (b): y = 19
(c)
5h
Answer (c): 5h
(d)
(5a – 2a) + (7f + 4f) = 3a + 11f M1 A1
Answer (d): 3a + 11f