Question

Solve the inequality. Graph and check your solution.

$-45>g-16$

Short answer

The solution for the inequality is $g<-29$.

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 d by solving the inequality

Since, the equality is $-45>g-16$.

Here, to simplify this inequality, adding $7$ to both side on the above

$\begin{array}{l}-45>g-16\\ -45+16>g-16+16\\ -29>g\\ g<-29\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $g<-29$.

So, this expression means that the value of g should be smaller than $-29$.

So, Put $-30,-31,-32,.........so on$ in $-45>g-16$to check whether the inequality hold or not

Put $g=-30$ in inequality,

$\begin{array}{l}-45>g-16\\ -45>-30-16\\ -45>-46\end{array}$

It holds the equation

Again, put $g=-31$ in equality

$\begin{array}{l}-45>g-16\\ -45>-31-16\\ -45>-47\end{array}$

It also holds the inequality.

So, the expression $g<-29$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $g<-29$ to get the proper graphical representation to know the points.