Chapter 3.4, Problem 37PPE

To determine

To Solve: The given inequality, $3\left(2+t\right)\ge 15-2t$ .

Answer to Problem 37PPE

  $t\ge \frac{9}{5}$

Explanation of Solution

Given information:

  $3\left(2+t\right)\ge 15-2t$

Concept Used:

We use the algebra of operations by adding or subtracting variable terms on both the sides. We also use distributive property given by

  $a\left(b-c\right)=ab-ac$

Also, multi-step inequality is solved by simplifying it into equivalent one step inequality.

Calculation:

As the given inequality is $3\left(2+t\right)\ge 15-2t$ , we solve it as follows:

Using distributive property, $a\left(b-c\right)=ab-ac$

  $\begin{array}{l}3\left(2+t\right)\ge 15-2t\\ 6+3t\ge 15-2t\end{array}$

Adding $2t$ both the sides, we get

  $\begin{array}{l}6+3t+2t\ge 15-2t+2t\\ 6+\left(3t+2t\right)\ge 15+\left(-2t+2t\right)\\ 6+5t\ge 15\end{array}$

Subtracting $6$ from both the sides we get

  $\begin{array}{l}6+5t-6\ge 15-6\\ 5t\ge 9\end{array}$

Dividing both the sides by $5$ , we get

  $\begin{array}{l}\frac{5t}{5}\ge \frac{9}{5}\\ t\ge \frac{9}{5}\end{array}$