Chapter 4, Problem 3CA

To determine

To calculate: To find which of the inequalities are equivalent

Answer to Problem 3CA

  $3x+6\le 8+2x;5x-5\ge 7x-9;-2-\frac{3}{2}x\ge -3-x$ inequalities are equivalent

Explanation of Solution

Given: Inequalities are

  $\begin{array}{l}3x+6\le 8+2x\\ 5x-5\ge 7x-9\\ 12-3x\le 18\\ -2-\frac{3}{2}x\ge -3-x\end{array}$

Calculation:

Simplify the inequality - $3x+6\le 8+2x$

  $\begin{array}{l}3x+6\le 8+2x\\ 3x-2x\le 8-6\\ x\le 2\end{array}$

Simplify the inequality - $5x-5\ge 7x-9$

  $\begin{array}{l}5x-5\ge 7x-9\\ 9-5\ge 7x-5x\\ 2x\le 4\\ x\le 2\end{array}$

Simplify the inequality - $12-3x\le 18$

  $\begin{array}{l}12-3x\le 18\\ 12-18\le 3x\\ 3x\ge -6\\ x\ge -2\end{array}$

Simplify the inequality - $-2-\frac{3}{2}x\ge -3-x$

  $\begin{array}{l}-2-\frac{3}{2}x\ge -3-x\\ -\frac{3}{2}x+x\ge -3+2\\ -\frac{1}{2}x\ge -1\\ \frac{x}{2}\le 1\\ x\le 2\end{array}$

Conclusion:

Hence, $3x+6\le 8+2x;5x-5\ge 7x-9;-2-\frac{3}{2}x\ge -3-x$ inequalities are equivalent