Chapter 4.2, Problem 70SR

To determine

To find: The value of variable $\left(b\right)$ for the equation $\frac{-8b-\left(-9\right)}{-10}=17$ and verify the obtained result.

Answer to Problem 70SR

The value of variable $\left(b\right)$ is equal to $-207$ .

Explanation of Solution

Given information: The given equation in variable $\left(b\right)$ is $\frac{-8b-\left(-9\right)}{-10}=17$ .

Calculation: Solving the giving equation,

  $\begin{array}{c}\frac{-8b-\left(-9\right)}{-10}=\mathrm{17......}\left(\text{1}\right)\\ \frac{-8b+9}{-10}=17\\ -8b+9=-\mathrm{170......}\left(\text{Cross-multiplying}\right)\\ \text{or, }8b=179\\ b=\frac{179}{8}\end{array}$

Verification of solution: Plugging for $b=\frac{179}{8}$ in (1),

  $\begin{array}{c}\frac{-8\left(\frac{179}{8}\right)-\left(-9\right)}{-10}=17\\ \frac{-179+9}{-10}=17\\ \frac{-170}{-10}=17\\ 17=\mathrm{17......}\left(\text{which is true}\right)\end{array}$

Hence, verified that $b=\frac{179}{8}$ is solution to the equation $\frac{-8b-\left(-9\right)}{-10}=17$ .