Chapter 0, Problem 35PG

To determine

To solve the inequality

Answer to Problem 35PG

  $m\ge 2$ is the solution.

Explanation of Solution

Given information:

  $2-m\le 6m-12$

Calculation:

The given inequality is $2-m\le 6m-12$

Subtracting 6m from both sides,

  $2-m-6m\le 6m-12-6m$

Solving the inequality,

  $-7m+2\le -12$

Subtracting -12 from both sides,

  $-7m+2-2\le -12-2$

Solving,

  $-7m\le -14$

Dividing equation by -7

  $\frac{-7m}{-7}\le \frac{-14}{-7}$

When divided by a negative number, inequality is flipped,

So,

  $m\ge 2$

Hence, $m\ge 2$ is the solution of the inequality.