Chapter 2.4, Problem 24P

Solve each equation. If the equation is an identity, write identity. If it has no solution, write no solution.

$-2(5.25+6.2x)=4(-3.1x+2.68)$

To determine

To solve an equation $-2\left(5.25+6.2x\right)=4\left(-3.1x+2.68\right)$ and write if the equation is an identity

Answer to Problem 24P

The equation $-2\left(5.25+6.2x\right)=4\left(-3.1x+2.68\right)$ has no solutions.

Explanation of Solution

Given information :

Given equation $-2\left(5.25+6.2x\right)=4\left(-3.1x+2.68\right)$

As we have $-2\left(5.25+6.2x\right)=4\left(-3.1x+2.68\right)$

  $\begin{array}{l}\Rightarrow -2\left(5.25+6.2x\right)=4\left(-3.1x+2.68\right)\\ \Rightarrow -10.5-12.4x=-12.4x+10.72\\ \Rightarrow -12.4x+12.4x=10.72+10.5\\ \Rightarrow 0=21.22\end{array}$

Which is not possible.

Hence, the equation $-2\left(5.25+6.2x\right)=4\left(-3.1x+2.68\right)$ has no solutions.