Question
8(2x - 5) - 6(3x - 7) = 1
✓
Answer
8(2x - 5) - 6(3x - 7) = 1On 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
$\frac{2\text{x}}{2}=\frac12$
$\text{x}=\frac12$
Verification:
Substituting $\text{x}=\frac12$ in L.H.S., we get
$=8\Big(2\times\frac{1}{2}-5\Big)-6\Big(3\times\frac{1}{2}-7\Big)$
$= 8(1 - 5) - 6(32 - 7)$
$= 8× (-4) - (6 \times 32) + (6 \times 7) $
$= -32 - 9 + 42 $
$= - 41 + 42 = 1 = \text{R.H.S.}$
$\text{L.H.S.} = \text{R.H.S.}$
Hence, verified.
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
$\frac{2\text{x}}{2}=\frac12$
$\text{x}=\frac12$
Verification:
Substituting $\text{x}=\frac12$ in L.H.S., we get
$=8\Big(2\times\frac{1}{2}-5\Big)-6\Big(3\times\frac{1}{2}-7\Big)$
$= 8(1 - 5) - 6(32 - 7)$
$= 8× (-4) - (6 \times 32) + (6 \times 7) $
$= -32 - 9 + 42 $
$= - 41 + 42 = 1 = \text{R.H.S.}$
$\text{L.H.S.} = \text{R.H.S.}$
Hence, verified.
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