Question

If $h\left( x \right)=3x+5$ and $h\left( a \right)=27$, then what is the value of a?
(a) $\dfrac{22}{3}$
(b) 22
(c) 3
(d) 6

Answer 1

Hint: We have given the equation in x as $h\left( x \right)=3x+5$. Now, substitute “a” in place of x in the equation then the equation will be in “a” and it is given that $h\left( a \right)=27$ so equating this substituted equation to 27 and solving this equation to get the value of “a”.

Complete step by step answer:
We have given the equation in x as follows:
$h\left( x \right)=3x+5$……….. Eq. (1)
We have also given the equation as follows:
$h\left( a \right)=27$
Now, if we substitute x in h(x) as “a” then h(x) becomes h(a) so substituting x as “a” in eq. (1) we get,
$h\left( a \right)=3a+5$
Equating the above equation to 27 because $h\left( a \right)=27$ we get,
$3a+5=27$……. Eq. (2)
Subtracting 5 on both the sides of the above equation we get,
$\begin{align}
  & 3a=27-5 \\
 & \Rightarrow 3a=22 \\
\end{align}$
Dividing 3 on both the sides of the above equation we get,
$a=\dfrac{22}{3}$
From the above calculations, we have found the value of “a” as $\dfrac{22}{3}$.

So, the correct answer is “Option a”.

Note: You can cross check the value of “a” that we have got above is by substituting this value of “a” in eq. (2) of the above solution we get,
$3a+5=27$
Substituting the value of “a” as $\dfrac{22}{3}$ in the above equation we get,
$3\left( \dfrac{22}{3} \right)+5=27$
3 will be cancelled out from the numerator and denominator of the left hand side of the above equation we get,
$\begin{align}
  & 22+5=27 \\
 & \Rightarrow 27=27 \\
\end{align}$
As you can see that L.H.S = R.H.S of the above equation so the value of “a” that we have solved above is correct.