Question

How do you solve and graph x – 3 > 7?

Answer 1

Hint: Rearrange the terms by taking the constant terms to the R.H.S. and leaving the terms containing the variable x to the L.H.S. Now, simplify the R.H.S. by simple addition or subtraction, whichever needed to get a particular numerical value. Leave the inequality sign as it is. Draw a line x = 10 and consider the suitable part of the graph according to the simplified inequality obtained.

Complete step-by-step solution:
Here, we have been provided with the inequality x – 3 > 7 and we are asked to solve it and draw the graph.
Now, rearranging the given inequality by taking the constant terms to the R.H.S. and leaving the terms containing the variable x in the L.H.S., we get,
\[\begin{align}
  & \Rightarrow x-3>7 \\
 & \Rightarrow x>7+3 \\
\end{align}\]
\[\Rightarrow x>10\] - (1)
Here, as you can see, the direction of the inequality sign does not change. This is because the direction of inequality sign only changes when we multiply or divide both the sides with a negative number or take reciprocal on both the sides.
Now, let us draw the graph of inequality obtained in (1). To do this first we have to remove the inequality sign and replace it with ‘=’ sign and draw the required line, so we have,
\[\Rightarrow x=10\]
Drawing the line x = 10, we get,

Now, considering equation (1), i.e., x > 10, here we can clearly see that we have to select that part of the graph in which x will be greater than 10. So, in the above graph we have to select the right side of the graph x = 10. Therefore, we have,

So, the above graph represents the graphical solution of our inequality.

Note: One may note that there are not many differences in solving and graphing an inequality and an equality. We need the help of equality while drawing the graph. One thing you can note is we do not have to consider the value x = 10 in our graph, so it will be better to use the dashed line instead of a solid line, however we have used a solid line. Always remember the rules of reversing the direction of inequality. The direction is only reversed when we take reciprocal or divide and multiply both the sides with a negative number.