Question

Solve the inequality. Graph and check your solution.

$x+3<7$

Short answer

The solution for the inequality is $x<4$.

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 $x+3<7$.

Here, to simplify this inequality, subtract $-3$to both side on the above

localid="1649246562465" $\begin{array}{l}x+3<7\\ x+3-3<7-3\\ x<4\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x<4$

So, this expression means that the value of x should be smaller than $4$.

So, Put localid="1649246589729" $3,2,1,0,-1,-2.......so on$in localid="1649246597593" $x+3<7$to check whether the inequality hold or not

Put localid="1649246628704" $x=2$in inequality,

localid="1649246623581" $\begin{array}{l}x+3<7\\ 2+3<7\\ 5<7\end{array}$

It holds the equation

Again, put localid="1649246642702" $x=1$in equality

localid="1649246662414" $\begin{array}{l}x+3<7\\ 1+3<7\\ 4<7\end{array}$

It also holds the inequality.

So, the expression localid="1649246672764" $x<4$correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression localid="1649246682879" $x<4$to get the proper graphical representation to know the points.