Question

Solve the inequality. Graph your solution.

$12-4q\ge 6q+2$

Short answer

The solution for the inequality is $q\le 1$.

Step-by-step solution

Step 1.  Apply the concept of Linear inequalities

In this type of inequality, Simply use the property of addition or subtraction of suitable number on both Left Hand Side & Right Hand Side to maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step 2.  Find the value of q by solving the inequality

Since, the equality is $12-4q\ge 6q+2$.

Here, to simplify this inequality, Take the variable and constant to the opposite side then $10$to both side of the equation.

$\begin{array}{l}12-4q\ge 6q+2\\ 12-2\ge 6q+4q\\ 10\ge 10q\\ 10q\le 10\\ \frac{10q}{10}\le \frac{10}{10}\\ q\le 1\end{array}$

Graphical Interpretation

Following is the graph of the expression $q\le 1$ to get the proper graphical representation to know the points.