If (x + 4) : (x +13)=(x-2) : (x+1), then find the
value of x.
(3 marks)
Answers
Answer:
-18
Step-by-step explanation:
multiple the ratio and equlate them it will -18 is your answer
Answer:
The value of x is - 22 / 10.
Step-by-step-explanation:
We have given that,
( x + 4 ) : ( x + 13 ) = ( x + 2 ) : ( x + 1 )
We have to find the value of x.
( x + 4 ) : ( x + 13 ) = ( x + 2 ) : ( x + 1 )
It is a ratio, i. e. division. So, we can write it like this,
[ ( x + 4 ) / ( x + 13 ) ] = [ ( x + 2 ) / ( x + 1 ) ]
⇒ ( x + 4 ) * ( x + 1 ) = ( x + 2 ) * ( x + 13 )
⇒ x² + x + 4x + 4 = x² + 13x + 2x + 26
⇒ x + 4x + 4 = 13x + 2x + 26 - - - [ Cancelling x² from both the sides ]
⇒ x + 4x - 13x - 2x = 26 - 4
⇒ 5x - 15x = 22
⇒ - 10x = 22
⇒ x = - 22 / 10
∴ The value of x is - 22 / 10.
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Verification:
We have,
( x + 4 ) : ( x + 13 ) = ( x + 2 ) : ( x + 1 )
x = - 22 / 10
Let's substitute the value of x in each term of both the sides of the given equation.
( x + 4 )
⇒ ( - 22 / 10 ) + 4
⇒ ( - 22 + 4 * 10 ) / 10
⇒ ( - 22 + 40 ) / 10
⇒ 18 / 10 - - ( 1 )
Now,
( x + 13 )
⇒ ( - 22 / 10 ) + 13
⇒ ( - 22 + 13 * 10 ) / 10
⇒ ( - 22 + 130 ) / 10
⇒ 108 / 10 - - ( 2 )
Now,
LHS = ( x + 4 ) : ( x + 13 )
⇒ LHS = ( 18 / 10 ) : ( 108 / 10 ) - - [ From ( 1 ) & ( 2 ) ]
⇒ LHS = [ ( 18 / 10 ) ÷ ( 108 / 10 ) ]
⇒ LHS = 18 / 10 * 10 / 108
⇒ LHS = 18 * 10 ÷ 10 * 108
⇒ LHS = 18 * 1 ÷ 108
⇒ LHS = 18 ÷ 108
⇒ LHS = 1 / 6
Now,
( x + 2 )
⇒ ( - 22 / 10 ) + 2
⇒ ( - 22 + 2 * 10 ) / 10
⇒ ( - 22 + 20 ) / 10
⇒ - 2 / 10
⇒ - 1 / 5 - - ( 3 )
Now,
( x + 1 )
⇒ ( - 22 / 10 ) + 1
⇒ ( - 22 + 1 * 10 ) / 10
⇒ ( - 22 + 10 ) / 10
⇒ - 12 / 10 - - ( 4 )
Now,
RHS = ( x + 2 ) : ( x + 1 )
⇒ RHS = ( - 1 / 5 ) : ( - 12 / 10 ) - - [ From ( 3 ) & ( 4 ) ]
⇒ RHS = [ ( - 1 / 5 ) ÷ ( - 12 / 10 ) ]
⇒ RHS = - 1 / 5 * - 10 / 12
⇒ RHS = 1 * 10 / 5 * 12
⇒ RHS = 10 / 60
⇒ RHS = 1 / 6
∴ LHS = RHS