Chapter 9, Problem 1MCP

To determine

To solve the inequality: $4-3x\ge 12-x$ .

Answer to Problem 1MCP

Solution:

The solution of the inequality is: $x\le -4$ , that is, $x\in \left(-\infty ,-4\right]$

Explanation of Solution

Given:

  $4-3x\ge 12-x$

Calculation:

We have been given that $4-3x\ge 12-x$

  $\begin{array}{c}4-3x\ge 12-x\\ 4-3x+x\ge 12-x+x\text{ Adding }x\text{ to both sides}\\ 4-2x\ge 12\\ 4-4-2x\ge 12-4\text{ Subtracting 4 to both sides}\\ -2x\ge 8\\ -\frac{2x}{2}\ge \frac{8}{2}\text{ Dividing by 2 to both sides}\\ -x\ge 4\\ \left(-1\right)-x\le \left(-1\right)4\text{ Multiplying by }-1\text{ to both sides}\\ x\le -4\end{array}$

Therefore, the solution of the inequality is: $x\le -4$ , that is, $x\in \left(-\infty ,-4\right]$ .

Conclusion:

The solution of the inequality is: $x\le -4$ , that is, $x\in \left(-\infty ,-4\right]$ .