Question

Solve the inequality. Graph and check your solution.

$1\ge x-9$

Short answer

The solution for the inequality is $x\le 10$.

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 $1\ge x-9$

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

$\begin{array}{l}1\ge x-9\\ 1+9\ge x-9+9\\ 10\ge x\\ x\le 10\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x\le 10$

So, this expression means that the value of x should be smaller than or equal to $10$.

So, Put$10,9,8,7.......so on$ in $1\ge x-9$ to check whether the inequality hold or not

Put $x=10$ in inequality,

$\begin{array}{l}1\ge x-9\\ 1\ge 10-9\\ 1\ge 1\\ 1=1\end{array}$

It holds the equation

Again, put $x=9$ in equality

$\begin{array}{l}1\ge x-9\\ 1\ge 9-9\\ 1\ge 0\end{array}$

It also holds the inequality.

So, the expression $x\le 10$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $x\le 10$ to get the proper graphical representation to know the points.