Chapter 8, Problem 11PT

To determine

To solve the given equation

Answer to Problem 11PT

  $t=\frac{10}{13}$

Explanation of Solution

Given:

Equation: $5(t^2-3t+2)=t(5t-2)$

Concept used:

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the given equation,

  $\Rightarrow 5(t^2-3t+2)=t(5t-2)$

Simplifying the equation,

Applying distributive property,

  $\begin{array}{l}\Rightarrow 5\times t^2-5\times 3t+5\times 2=t\times 5t-t\times 2\\ \Rightarrow 5t^2-15t+10=5t^2-2t\end{array}$

Subtracting $5t^2$ on both sides and simplifying,

  $\begin{array}{l}\Rightarrow 5t^2-15t+10-5t^2=5t^2-2t-5t^2\\ \Rightarrow -15t+10=-2t\end{array}$

Subtracting $10$ on both sides and simplifying,

  $\begin{array}{l}\Rightarrow -15t+10-10=-2t-10\\ \Rightarrow -15t=-2t-10\end{array}$

Adding $2t$ on both sides,

  $\begin{array}{l}\Rightarrow -15t+2t=-2t-10+2t\\ \Rightarrow -13t=-10\end{array}$

Dividing − 13 on both sides and simplifying,

  $\begin{array}{l}\Rightarrow \frac{-13t}{-13}=\frac{-10}{-13}\\ \Rightarrow t=\frac{10}{13}\end{array}$

Conclusion:

Therefore, the solution to the given equation is $t=\frac{10}{13}.$