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Question

Solve each of the following equations and check your answers:
6(1 4x) + 7(2 + 5x) = 53

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Solution

6(1 4x) + 7(2 + 5x) = 53
On expanding the brackets, we get
⇒ (6×1) - (6 × 4x) + (7 ×2) + (7×5x) = 53
⇒ 6 - 24x + 14 + 35x = 53
⇒ 6 + 14 + 35x - 24x = 53
⇒ 20 + 11x = 53
Subtracting 20 from both sides, we get
⇒ 20 + 11x - 20 = 53 - 20
⇒ 11x = 33
⇒ Dividing both sides by 11, we get
11x11 = 3311
⇒ x = 3


Verification:
Substituting x = 3 in LHS, we get
=
6(1 4×3) + 7(2 + 5×3)
= 6(1 − 12) + 7(2 + 15)
= 6(−11) + 7(17)
= −66 + 119 = 53 = RHS
LHS = RHS
Hence, verified.

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