Chapter 4.5, Problem 41PPS

To determine

To solve and check: the given equation

Answer to Problem 41PPS

The required solution is $x=-14.5$

Explanation of Solution

Given: $\frac{-2x+5}{2}=17$

Calculation:

To solve equation and check the solution

  $\frac{-2x+5}{2}=17$

Multiply both sides of equation with 2

  $\begin{array}{l}-2x+5=17\cdot 2\\ -2x+5=34\end{array}$

Add both sides of equation with $-5$

  $\begin{array}{l}-2x+5-5=34-5\\ -2x=29\end{array}$

Divide both sides of equation with $-2$

  $\begin{array}{l}x=-\frac{29}{2}\\ x=-14.5\end{array}$

Solution:- $x=-14.5$

Check

Substitute $x=-14.5$ in $\frac{-2x+5}{2}=17$

  $\begin{array}{l}\frac{-2\left(-14.5\right)+5}{2}=17\\ \frac{29+5}{2}=17\\ 17=17\end{array}$

Hence verified. So solution is $x=-14.5$

Conclusion:

Therefore, the required solution is $x=-14.5$