Chapter 4.5, Problem 34PPS

To determine

To solve and check: the given equation

Answer to Problem 34PPS

The required solution is $x=1.6$

Explanation of Solution

Given: $\frac{3}{4}x+1.5=2.7$

Calculation:

To solve equation and check the solution

  $\frac{3}{4}x+1.5=2.7$

Add both sides of equation with $-1.5$

  $\begin{array}{l}\frac{3}{4}x+1.5-1.5=2.7-1.5\\ \frac{3}{4}x=1.2\end{array}$

Multiply both sides of equation with $\frac{4}{3}$

  $x=1.2\cdot \frac{4}{3}$

Divide out the common terms

  $\begin{array}{l}x=\frac{\cancel{3}\cdot 0.4\cdot 4}{\cancel{3}}\\ x=1.6\end{array}$

Solution:- $x=1.6$

Check

Substitute $x=1.6$ in $\frac{3}{4}x+1.5=2.7$

  $\frac{3}{4}\left(1.6\right)+1.5=2.7$

Divide out the common terms

  $\begin{array}{l}\frac{3}{4}\left(\mathrm{4.0.4}\right)+1.5=2.7\\ 2.7=2.7\end{array}$

Hence verified. So solution is $x=1.6$

Conclusion:

Therefore, the required solution is $x=1.6$