Question

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

Answer 1

Hint: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,
$$x>-{\displaystyle \frac{6}{2}}$$
$$\Rightarrow x>-3$$.
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.