Chapter 2.7, Problem 64PPSE

Solution

To Solve:

The given inequality.

To Graph:

The solution on a number line.

  $-3\ge t$

Given:

  $5-2t\ge 11$ .

Concepts Used:

Adding an expression to the expressions on both sides of an inequality does not affect the inequality.

Subtracting an expression from the expressions on both sides of an inequality does not affect the inequality.

Dividing the expressions on both sides of an inequality by a positive quantity does not affect the inequality.

Calculations:

Subtract $11$ from both sides of the given inequality $5-2t\ge 11$ :

  $\begin{array}{c}5-2t\ge 11\\ 5-11-2t\ge 0\\ -6-2t\ge 0\end{array}$

Add $2t$ to both sides of the inequality $-6-2t\ge 0$ :

  $\begin{array}{c}-6-2t\ge 0\\ -6\ge 2t\end{array}$

Divide both sides of the inequality $-6\ge 2t$ by the positive number $2$ :

  $\begin{array}{c}-6\ge 2t\\ -\frac{6}{2}\ge t\\ -3\ge t\end{array}$

Graph:

Graph the solution $-3\ge t$:

  

Conclusion:

  $-3\ge t$ is the solution of the given inequality and it is graphed on the number line as shown above.