Question

How do you solve for $g$ in \[S = \dfrac{1}{2}gt\] ?

Answer 1

Hint: In this question, we have to find out the solution for g from the given equation. First, we need to put the required value on the left side and need to put all the other values on the right side of the equality sign. We will apply cross multiplication to the equation to find the required solution. Basically, shift all the letters and constants to the other side, such that only g remains on one side.

Complete step-by-step solution:
It is given that, \[S = \dfrac{1}{2}gt\] .
We have to find out the solution for g in \[S = \dfrac{1}{2}gt\] .
First, we need to put the required value on the left side and need to put all the other values on the right side of the equality sign.
We will apply cross multiplication to the equation to find the required solution.
Applying cross multiplication, we get,
\[ \Rightarrow 2S = gt\] .
We can write it as,
\[ \Rightarrow gt = 2S\]
Now we need to put only g on the left side, for doing that we need to divide both sides by t.
Dividing both sides by t we get,
\[ \Rightarrow \dfrac{{gt}}{t} = \dfrac{{2S}}{t}\] .
i.e., \[g = \dfrac{{2S}}{t}\]

Hence, the solution for g in \[S = \dfrac{1}{2}gt\] is \[g = \dfrac{{2S}}{t}\].

Note: Cross multiplication:
In Mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of variables.
In practice, the method of cross-multiplying means that we multiply the numerator of each (or one) side by the denominator of the other side, effectively crossing the items over:
If we apply it to the equation, $\dfrac{a}{b} = \dfrac{c}{d}$ will be like this, \[\dfrac{a}{b} \nearrow \dfrac{c}{d},\dfrac{a}{b} \nwarrow \dfrac{c}{d}\] .