Answer

Verified

372.6k+ views

**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.

Recently Updated Pages

What are the Advantages and Disadvantages of Algorithm

How do you write 0125 in scientific notation class 0 maths CBSE

The marks obtained by 50 students of class 10 out of class 11 maths CBSE

Out of 30 students in a class 6 like football 12 like class 7 maths CBSE

Explain the law of constant proportion in a simple way

How do you simplify left 5 3i right2 class 12 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE