Chapter 1.5, Problem 11E

To determine

To solve the literal equation for y .

Answer to Problem 11E

  $y=18x-12$

Explanation of Solution

Given:

Equation: $2+\frac{1}{6}y=3x+4$

Concept used:

Literal equation is an equation is which one of the variable is entirely written in terms of the other.

It establishes a relationship between the variables.

Distributive property: $a\cdot b+a\cdot c=a(b+c)$

Calculation:

Consider the given equation and follow the steps as below to find the literal equation of y :

  $\Rightarrow 2+\frac{1}{6}y=3x+4$

Simplifying the equation,

  $\begin{array}{l}\Rightarrow \frac{2\times 6}{6}+\frac{1}{6}y=3x+4\\ \Rightarrow \frac{12+y}{6}=3x+4\end{array}$

Multiplying 6 on both sides,

  $\begin{array}{l}\Rightarrow \frac{6(12+y)}{6}=6(3x+4)\\ \Rightarrow 12+y=6(3x+4)\end{array}$

Applying distributive property to the right hand side,

  $\Rightarrow 12+y=18x+24$

Subtracting12 on both sides and simplifying,

  $\begin{array}{l}\Rightarrow 12+y-12=18x+24-12\\ \Rightarrow y=18x-12\end{array}$

Conclusion:

Thus, the literal equation for y is $y=18x-12.$