Question

Solve the inequality. Graph and check your solution.

$f+1\ge -8$

Short answer

The solution for the inequality is $f\ge -9$.

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 f by solving the inequality

Since, the equality is $f+1\ge -8$.

Here, to simplify this inequality, subtract $1$to both side on the above.

$\begin{array}{l}f+1\ge -8\\ f+1-1\ge -8-1\\ f\ge -9\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $f\ge -9$.

So, this expression means that the value of f should be greater than or equal to $-9$.

So, Put $-8,-7,-6,.........so on$ in $f+1\ge -8$to check whether the inequality hold or not

Put $f=-8$ in inequality,

$\begin{array}{l}f+1\ge -8\\ -8+1\ge -8\\ -7\ge -8\end{array}$

It holds the equation

Again, put $f=-7$ in equality

$\begin{array}{l}f+1\ge -8\\ -7+1\ge -8\\ -6\ge -8\end{array}$

It also holds the inequality.

So, the expression $f\ge -9$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $f\ge -9$ to get the proper graphical representation to know the points.