Question

How do you graph the inequality $2x > - 6$ and $x - 4 < 3$ ?

Answer 1

We simplify the given inequality. Then we draw the graph for a simplified equation. We use intercept form to draw the graph. That is we find the coordinate of the given equation lying on the line of x- axis, we can find this by substituting the value of ‘y’ is equal to zero (x-intercept). Similarly we can find the coordinate of the equation lying on the line of y- axis, we can find this by substituting the value of ‘x’ equal to zero (y-intercept). After drawing the graph we can check in which region the inequality satisfies. We will have a two line parallel to the y-axis.

Complete step by step answer:
Given, $2x > - 6$ and $x - 4 < 3$.
Now $2x > - 6$
Divide the whole inequality by 2,
$x > - \dfrac{6}{2}$
$\Rightarrow x > - 3$.
Now take $x - 4 < 3$
Add 4 on both side of the inequality,
$x - 4 + 4 < 3 + 4$
$\Rightarrow x < 7$
Now we draw the graph for $x = - 3$ and $x = 7$. For $x = - 3$ we don’t have a variable ‘y’. So whatever the values we give for ‘y’, the value of ‘x’ will be $- 3$. Thus the coordinates are $( - 3,1),( - 3,2)( - 3,3)( - 3, - 1)( - 3, - 2)$ and so on. For $x = 7$ we don’t have a variable ‘y’. So whatever the values we give for ‘y’, the value of ‘x’ will be $7$. Thus the coordinates are $(7,1),(7,2)(7,3)(7, - 1)(7, - 2)$ and so on.Let’s plot a graph for these coordinates. We take scale x-axis= 1 unit = 1 units and y-axis= 1 unit = 1 units.

In the above graph the shaded region is the solution of $2x > - 6$. Also if we take a point lying on the line $x = - 3$ the inequality $2x > - 6$ is not satisfied.

In the above graph the shaded region is the solution of $x - 4 < 3$. Also if we take a point lying on the line $x = 7$ the inequality $x - 4 < 3$ is not satisfied. In the above graph the shaded region is the solution of the given inequality.

Note: A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.