Question

Find out which operation must be done on both sides of these equations in order to solve them. 1.x+9=11,2.x-4=9,3.8x=24 and x/6=3​

Answer 1

Solution

$\tt (1)x + 9 = 11$

First to find the value of x we need to eliminate constants in LHS

To eliminate x :

→ If in LHS addition ( + ) opertion is there between constant and variable, then subtraction operation should be done on both sides to solve x + 9 = 11

And 9 i.e constant in LHS only should be subtracted on both sides.

Solving x + 9 = 11

$\implies x + 9 = 11$

Subtracting 9 on both sides

$\implies \boxed{x = 2}$

$\tt (2)x - 4 = 9$

To eliminate x :

→ If in LHS subtraction ( - ) opertion is there between constant and variable, then addition operation should be done on both sides to solve x + 4 = 9

And 4 i.e constant in LHS only should be added on both sides.

Solving x - 4 = 9

$\implies x - 4 = 9$

Adding 4 on both sides

$\implies x - 4 + 4= 9 + 4$

$\implies \boxed{x =13}$

$\tt (3)8x = 24$

To eliminate x :

→ If in LHS multiplication ( * ) opertion is there between constant and variable, then division operation should be done on both sides to solve 8x = 24

And 8 i.e constant in LHS only should be divided on both sides.

Solving 8x = 24

$\implies 8x = 24$

Dividing 8 on both sides

$\implies \dfrac{8x}{8} = \dfrac{24}{8}$

$\implies \boxed{x = 3}$

$\tt (4) \dfrac{x}{6} = 3$

To eliminate x :

→ If in LHS division ( / ) opertion is there between constant and variable, multiplication operation should be done on both sides to solve x/6 = 3

And 6 i.e constant in LHS only should be multiplied on both sides.

Solving x/6 = 6

$\implies \dfrac{x}{6} = 3$

Mutiplying by 6 on both sides

$\implies \dfrac{x}{6} \times 6 = 3 \times 6$

$\implies \boxed{x = 18}$

Answer 2

Question :-

Given above ↑

Answer :-

(1) x = 2

(2) x = 13

(3) x = 3

(4) x = 18

Explanation for each question :-

(1) x + 9 = 11

For eliminating 9 which is with "x" subtract 9 on both sides,

→ x + 9 - 9 = 11 - 9

→ x = 2

__________________________

(2) x - 4 = 9

Adding 4 on both sides ,

→ x - 4 + 4 = 9 + 4

→ x = 13

__________________________

(3) 8x = 24

Divided by 8 on both sides ,

→ 8x/8 = 24/8

→ x = 3

__________________________

(4) x/6 = 3

multiplying by 6 on both sides ,

→ 6 • x/6 = 6 • 3

→ x = 18

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Hope it helps you : )