Question

Solve the inequality. Graph and check your solution.

$-6\le x-9$

Short answer

The solution for the inequality is $x\ge 3$.

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 Sideto maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step -2 – Find the value of x by solving the inequality

Since, the equality is $-6\le x-9$.

Here, to simplify this inequality, adding $9$ to both side on the above

$\begin{array}{l}-6\le x-9\\ -6+9\le x-9+9\\ 3\le x\\ x\ge 3\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x\ge 3$

So, this expression means that the value of x should be greater than or equal to $3$.

So, Put $4,5,6,.....\&..so on$ in $-6\le x-9$ to check whether the inequality hold or not

Put $x=4$ in inequality,

$\begin{array}{l}-6\le x-9\\ -6\le 4-9\\ -6\le -5\end{array}$

It holds the equation

Again, put $x=5$in equality

$\begin{array}{l}-6\le x-9\\ -6\le 5-9\\ -6\le -4\end{array}$

It also holds the inequality.

So, the expression $x\ge 3$correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $x\ge 3$ to get the proper graphical representation to know the points.