Question

Solve the inequality. Graph and check your solution.

$x+4<5$

Short answer

The solution for the inequality is $x<1$.

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 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 $x+4<5$.

Here, to simplify this inequality, subtract $-4$to both side on the above

$\begin{array}{l}x+4<5\\ x+4-4<5-4\\ x<1\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x<1$

So, this expression means that the value of x should be smaller than$1$.

So, Put $0,-1,-2.......so on$in $x+4<5$to check whether the inequality hold or not

Put $x=0$in inequality,

$\begin{array}{l}x+4<5\\ 0+4<5\\ 4<5\end{array}$

It holds the equation

Again, put $x=-1$in equality

$\begin{array}{l}x+4<5\\ -1+4<5\\ 3<5\end{array}$

It also holds the inequality.

So, the expression $x<1$correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $x<1$ to get the proper graphical representation to know the points.