Chapter 7.7, Problem 30E

To determine

To find: the solution of equation $-5y-13=7-15y$ and check the solution

Answer to Problem 30E

The solution of equation is $y=2$

Explanation of Solution

Given information: Consider, the equation $-5y-13=7-15y$ provided in the question

Calculation:

To evaluate the value of expression $-5y-13=7-15y$ , it is needed to combine like terms

Therefore, the value of expression is obtained as:

  $\begin{array}{l}-5y-13=7-15y\\ \text{add}15y\text{in}\text{each}\text{side}\\ \Rightarrow -5y-13+15y=7-15y+15y\\ \Rightarrow 10y-13=7\\ \text{add}13\text{in}\text{each}\text{side}\\ \Rightarrow 10y-13+13=7+13\\ \Rightarrow 10y=20\\ \text{divide}\text{each}\text{side}\text{by}10\\ \Rightarrow \frac{10y}{10}=\frac{20}{10}\\ \Rightarrow y=2\end{array}$

Check:

  $\text{substitute}y=2\text{in}\text{given}\text{equation}$

  $\begin{array}{l}\Rightarrow -\text{5(2)-13=7-15(2)}\\ \Rightarrow -\text{10-13=7-30}\\ \Rightarrow -23\text{=}\text{-23}\end{array}$

Therefore, Left hand side =Right hand side.

Hence,

The solution of equation is $y=2$