Chapter 2.4, Problem 26P

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

$0.5t+0.25(t+16)=4+0.75t$

To determine

To solve an equation $0.5t+0.25\left(t+16\right)=4+0.75t$ and write if the equation is an identity

Answer to Problem 26P

The equation $0.5t+0.25\left(t+16\right)=4+0.75t$ is an identity.

Explanation of Solution

Given information :

Given equation $0.5t+0.25\left(t+16\right)=4+0.75t$

As we have $0.5t+0.25\left(t+16\right)=4+0.75t$

  $\begin{array}{l}\Rightarrow 0.5t+0.25t+4=4+0.75t\\ \Rightarrow 0.75t=4-4+0.75t\\ \Rightarrow 0.75t=0.75t\end{array}$

Thus, the equation is true for every value of $\text{'}t\text{'}$ .

Hence, the equation $0.5t+0.25\left(t+16\right)=4+0.75t$ is an identity.