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Laws of Exponents

1 x+5=3 x2 7 ...

Question

(1) x + 5 = 3x
(2) 7x = 20 − x
(3) 6(x − 1) = 5(x + 1)
(4) 2x + 3 = 3(x − 1)

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Solution

(1) x + 5 = 3x
$⟹$ 3x - x = 5
⇒ 5 = 2x
∴ x = $\frac{5}{2}$
(2) 7x = 20 − x
⇒ 8x = 20
⇒ x = $\frac{20}{8}$
∴ x = $\frac{5}{2}$
(3) 6(x − 1) = 5(x + 1)
⇒ 6x − 6 = 5x + 5
⇒ − 6 = − x + 5
⇒ − 11 = − x
∴ x = 11
(4) 2x + 3 = 3(x − 1)
⇒ 2x + 3 = 3x − 3
⇒ 3 = x − 3
∴ x = 6

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