Question

Four added to twice a number yield $\dfrac{26}{5}$. Find the number?

Answer 1

Hint: The easiest way to write algebraic expressions from a sentence is to look for the unknown quantity, and assume it to be a variable (say \[x\]). And then, we must perform suitable operations, as needed. Once the equation is formed, we can solve it to find the value of $x$.

Complete step-by-step solution:
The verbal representation of required algebraic expression is given as “four added to twice a number yield $\dfrac{26}{5}$” Here, we do not have any information regarding the “number” mentioned in our above statement.
So, we are assuming this “number” to be \[x\].
We can see that the first part of our statement says “twice a number”, that is, the number $x$ is multiplied by 2.
And so, our expression now becomes \[\left( 2x \right)\].
We now have, “four added to twice a number”. So, now by using our past steps, we can also write this statement as “four added to \[\left( 2x \right)\]”.
So, our expression now evaluates to \[\left( 4+2x \right)\].
The complete statement is “four added to twice a number yield $\dfrac{26}{5}$”. Thus, we can write,
$4+2x=\dfrac{26}{5}$.
On subtracting 4 on both sides, we get
$2x=\dfrac{26}{5}-4$.
We can take the LCM on right hand side, and thus, we get
$2x=\dfrac{26-20}{5}$.
$\Rightarrow 2x=\dfrac{6}{5}$.
We can now cancel 2 from both sides,
$x=\dfrac{3}{5}$.
Hence, our required number is \[\dfrac{3}{5}\].

Note: We must carefully read that on which part of our expression, any specified operation is taking place. Also, we must also take care to always use any operation on both sides of our equation. For unknown value we assume a variable and write the linear equation to find the value.