Question

Consider the given expression: $\dfrac{\left( x+1 \right)}{\left( 2x+3 \right)}=\dfrac{3}{8}$ , then $x=$
(a) $\dfrac{1}{4}$
(b) $\dfrac{1}{3}$
(c) $\dfrac{1}{6}$
(d) $\dfrac{1}{2}$

Answer 1

Hint: To find the value of x from $\dfrac{\left( x+1 \right)}{\left( 2x+3 \right)}=\dfrac{3}{8}$ , we have to first perform cross multiplication. Then we have to apply distributive property. We have to collect the terms with variables on one side and constants on the other. Then perform the required operations and solve for x.

Complete step by step solution:
We have to find the value of x from $\dfrac{\left( x+1 \right)}{\left( 2x+3 \right)}=\dfrac{3}{8}$ . We have to cross multiply. This is done by multiplying the denominator of the RHS with the numerator of the LHS and multiplying the denominator of the LHS with the numerator of the RHS.
$\Rightarrow 8\left( x+1 \right)=3\left( 2x+3 \right)$
Now, let us apply the distributive property on the terms on both sides.
$\Rightarrow 8x+8=6x+9$
We have to collect the terms containing the variables on one side and constants on the other. For this, we have to take 6x to the LHS and 8 to the RHS.
$\Rightarrow 8x-6x=9-8$
Now, let us perform the subtraction.
$\Rightarrow 2x=1$
Let us take the coefficient of x to the RHS.
$\Rightarrow x=\dfrac{1}{2}$

So, the correct answer is “Option d”.

Note: Students must know to solve algebraic expressions and the rules associated with it. They must know to change the signs of positive and negative terms when these terms are moved from one side to the other. Likewise, the product term will be the divisor when moved from one side to the other and the divisor will be the multiplier when it is moved from one side to the other. Students must know the laws of algebraic expressions. These laws include commutative, associative and distributive.