Chapter 2.4, Problem 7P

Solve each equation. Check your answer.

$17-9y=-3+16y$

To determine

To solve: The given equation .

Answer to Problem 7P

  $y=\frac{4}{5}$

Explanation of Solution

Given information: $17-9y=-3+16y$

Solution:

By adding 9y to both sides of the equation, we get

$\begin{array}{l}17-9y+9y=-3+16y+9y\\ 17=-3+25y\end{array}$

By adding 3 to both sides of the equation, we get

$\begin{array}{l}17+3=-3+25y+3\\ 20=25y\\ 25y=20\end{array}$

Dividing both sides of the equation by 25, we get

$\begin{array}{l}y=\frac{20}{25}\\ y=\frac{4}{5}\end{array}$

Thus, solution of given equation is

$y=\frac{4}{5}$

VERIFICATION:

To check that $y=\frac{4}{5}$ is solution of the equation, we substitute $y=\frac{4}{5}$ in both sides of equation.

$\begin{array}{l}LHS=17-9y=17-9\times \frac{4}{5}=\frac{49}{5}\\ RHS=-3+16y=-3+16\times \frac{4}{5}=\frac{49}{5}\end{array}$

Since, $LHS=RHS$

Hence, solution is correct.