Question

Solve the following equations
(g) 3(x + 1) = 6
(h) 4( x- 2) = -8
(i) 3x + 8 = 5x + 2
(j) (1/3)x + 11 = 14
(k) (x-5)/4 = 3
(l) (z+3)/4 = 17

Class - IV
LINEAR EQUATIONS

class - VI
LINEAR EQUATIONS

Answer 1

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Here is your answer

(g) 3(x + 1) = 6

$3(x + 1) = 6 \\ \\ 3x + 3 = 6 \\ \\ 3x = 6 - 3 \\ \\ 3x = 3 \\ \\ x = \frac{3}{3} \\ \\ x = 1$

(h) 4(x - 2) = -8

$4(x - 2) = - 8 \\ \\ 4x - 8 = - 8 \\ \\ 4x = - 8 + 8 \\ \\ 4x = 0 \\ \\ so \\ \\ x = 0$
(i) 3x + 8 = 5x + 2

$3x + 8 = 5x + 2 \\ \\ 8 - 2 = 5x - 3x \\ \\ 6 = 2x \\ \\ x = \frac{6}{2} \\ \\ x = 3$
(j) (1/3)x + 11 = 14

$( \frac{1}{3} )x + 11 = 14 \\ \\ \frac{x}{3} + 11 = 14 \\ \\ \frac{x}{3} = 14 - 11 \\ \\ \frac{x}{3} = 3 \\ \\ x = 3 \times 3 \\ \\ x = 9$
(k) (x - 5)/4 = 3

$\frac{(x - 5)}{4} = 3 \\ \\ x - 5 = 3 \times 4 \\ \\ x - 5 = 12 \\ \\ x = 12 + 5 \\ \\ x = 17$
(l) (z + 3)/4 = 17

$\frac{(z + 3)}{4} = 17 \\ \\ z + 3 = 17 \times 4 \\ \\ z + 3 = 68 \\ \\ z = 68 - 3 \\ \\ z = 65$

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Answer 2

SOLUTION :

(g) 3(x + 1) = 6

⇒ $\frac{3(x+1)}{ \bf{3} }$ = $\frac{6}{ \bf{3} }$  [Divide both sides by 3 ]

⇒ x + 1 = 2

⇒ x + 1 - 1 = 2 - 1  [ Adding -1 to both sides ]

⇒ x = 1

∴ x = 1 is the solution of the given equation ( 3(x + 1) = 6 )

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(h) 4( x - 2) = -8

⇒ $\frac{4(x - 2)}{ \bf{4} }$ = $\frac{-8}{ \bf{4} }$  [ Divide both sides by 4 ]

⇒ x - 2 = -2

⇒ x - 2 + 2 = -2 + 2  [ Adding 2 to both sides ]

⇒ x = 0

∴ x = 0 is the solution of the given equation (  4( x - 2) = -8 )

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(i) 3x + 8 = 5x + 2  

⇒ 3x + 8 - 2 = 5x + 2 - 2  [ Adding -2 to both sides ]

⇒ 3x + 6 = 5x

⇒ 6 + 3x - 3x = 5x - 3x [ Adding -3x to both sides ]

⇒ 6 = 2x

⇒ $\frac{6}{ \bf{2} }$ =  $\frac{2x}{ \bf{2} }$

⇒ 3 = x

∴ x = 3 is the solution of the given equation (  3x + 8 = 5x + 2  )

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(j) (1/3)x + 11 = 14

⇒ $\frac{1}{3} \times x$ + 11 = 14

⇒ $\frac{x}{3}$ + 11 = 14

⇒ $\frac{x}{3}$ + 11 - 11 = 14 - 11 [ Adding -11 to both sides ]

⇒ $\frac{x}{3}$ = 3

⇒ $\frac{x}{3} \times \bf{3}$ = 3 × 3  [Multiply both sides by 3 ]

⇒ x = 9

∴ x = 9 is the solution of the given equation (  (1/3)x + 11 = 14  )

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(k) (x-5)/4 = 3  

⇒ $\frac{(x-5)}{4} \times 4$ = 3 × 4   [ Multiply both sides by 4 ]

⇒ x - 5 = 12

⇒ x - 5 + 5 = 12 + 5

⇒ x = 17

∴ x = 17 is the solution of the given equation ( (x-5)/4 = 3  )

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(l) (z+3)/4 = 17

⇒  $\frac{(z+3)}{4} \times 4$ = 17 × 4   [ Multiply both sides by 4 ]

⇒ z + 3 = 68

⇒ z + 3 - 3 = 68 - 3

⇒ z = 65

∴ z = 65 is the solution of the given equation ( (z+3)/4 = 17  )

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