Question

(x+3): (x+11)=(x-2):(x+1) What is the value of x​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since ,the given Equation are in the ratio form so,first we have to make into fractional form then we will find the find value of x.

$\sf = > \dfrac{x + 3}{x + 11} = \dfrac{x + 2}{x + 1}$

Now,the given equation is in the form of fraction

Cross multiply to both sides

$\sf = > (x + 3)(x + 1) = (x + 11) (x+ 2)$

➙x(x+1)+3(x+1)=x(x+2)+11(x+2)

➙x²+x+3x+3=x²+2x+11x+22

➙x²+4x+3=x²+13x+22

Since,x²lies on both sides so,it gets cancelled

➙4x+3=13x+22

Solve for x

➙4x-13x= 22-3

➙-9x= 19

➙x= -19/9

Check:-

➙ -9x = 19

➙ -9× -19/9

➙-1× -19

= 19

Since,LHS = RHS(Verified)

Answer 2

Since ,the given Equation are in the ratio form so,first we have to make into fractional form then we will find the find value of x.

= > {x + 3}{x + 11} = \{x + 2}{x + 1}

=> x+11

x+3

x+1

x+2

Now,the given equation is in the form of fraction

Cross multiply to both sides

= > (x + 3)(x + 1) = (x + 11) (x+ 2)=>(x+3)(x+1)=(x+11)(x+2)

➙x(x+1)+3(x+1)=x(x+2)+11(x+2)

➙x²+x+3x+3=x²+2x+11x+22

➙x²+4x+3=x²+13x+22

Since,x²lies on both sides so,it gets cancelled

➙4x+3=13x+22

Solve for x

➙4x-13x= 22-3

➙-9x= 19

➙x= -19/9

Check:-

➙ -9x = 19

➙ -9× -19/9

➙-1× -19

= 19

Since,LHS = RHS(Verified)