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Question

Solve each of the following equations and check your answers:
8(2x 5) − 6(3x − 7) = 1

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Solution

8(2x 5) − 6(3x − 7) = 1
On expanding the brackets, we get
⇒ (8×2x) - (8 × 5) - (6 × 3x) + (-6)×(-7) = 1
⇒ 16x - 40 - 18x + 42 = 1
⇒ 16x - 18x + 42 - 40 = 1
-2x + 2 = 1
Subtracting 2 from both sides, we get
-2x + 2 - 2 = 1 - 2
-2x = -1
Multiplying both sides by -1, we get
-2x ×(-1) = -1×(-1)
⇒ 2x = 1
Dividing both sides by 2, we get
2x2 = 12
⇒ x = 12

Verification:
Substituting x = 12 in LHS, we get
= 8(2×12 - 5) - 6(3×12 − 7)

= 8(1 − 5) − 6(32 − 7)

= 8×(−4) − (6 ×32) + (6 ×7)
= −32 − 9 + 42 = − 41 + 42 = 1 = RHS
LHS = RHS
Hence, verified.

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