Question

Solve :-
1.) Fifteen less than a no. is 9. Find the no.
2.) A number decreased by 30 is same as 14 decreased by 3 times the number. Find
the no.
3.) 3x + 4 = 22
4.) 2( 4x -1) = 20
5.) ___ number can be added to both the sides of the equation.

Answer 1

ANS 1. -6

ANS 2. A number (x) decreased by 30 (x - 30) is the same as (=) 14 decreased by 3 times the number (14 - 3x).

ANS 3. 3×6+4=22

ANS 4. 2(4x-1 )=20

8x-2=20

ANS 5. Any Number

Answer 2

Solution :-  

i ) Fifteen less than a number is 9. Find the number.

$\sf \implies x -15 = 9$

$\sf \implies x = 9 + 15$

$\sf \implies x = 24$

Verification :-

~LHS

$\sf \implies 24-15$

$\sf \implies 9$

~RHS

$\sf \implies 9$

LHS = RHS  

→ Hence , verified.

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ii ) A number decreased by 30 is same as 14 decreased by 3 times the number. Find the number

Let the required no. be ‘x’  

$\sf \implies 30-x = 3x-14$

$\sf \implies 3x+x = 30+14$

$\sf \implies 4x = 44$

$\sf \implies x = \dfrac{44}{4}$  

$\sf \implies x = 11$

Verification :-  

~LHS  

$\sf \implies 30-11$

$\sf \implies 19$

~RHS  

$\sf \implies 3(11) -14$

$\sf \implies 33-14$

$\sf \implies 19$

LHS = RHS  

→ Hence, verified  

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iii)  3x + 4 = 22  

$\sf \implies 3x + 4 = 22$  

$\sf \implies 3x = 22-4$  

$\sf \implies 3x = 18$

$\sf \implies x = \dfrac{18}{3}$  

$\sf \implies x = 6$

Verification :-  

~LHS  

$\sf \implies 3(6) + 4$

$\sf \implies 18 + 4$

$\sf \implies 22$

~RHS  

$\sf \implies 22$

LHS = RHS  

→ Hence, verified  

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iv) 2( 4x - 1 ) = 20  

$\sf \implies 2(4x-1) = 20$

$\sf \implies 4x-1 = \dfrac{20}{2}$

$\sf \implies 4x-1 = 10$

$\sf \implies 4x = 10+1$

$\sf \implies 4x = 11$

$\sf \implies x = \dfrac{11}4}$

Verification :-  

~LHS  

$\sf \implies 2 \bigg\{ \dfrac{11}{4} \times 4 -1 \bigg\}$

$\sf \implies 2( 11 -1)$

$\sf \implies 2( 10 )$

$\sf \implies 20$

~RHS  

$\sf \implies 20$

LHS = RHS  

→ Hence, verified  

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iv) Zero can be added on the both sides of the equation.

• Because, it is the additive identity and if we add zero to anything it will result the same.

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