Question

How do you solve and graph $ - x - 3 < - 5?$

Answer 1

Hint:Firstly, solve the given inequality for the value of $x$ then replace the inequality with equality sign and then draw the graph for the equation. Now pick up any point other than on the graph of the equation and check it on the inequality, if it satisfies it then shade portion of the point’s side and if not then shade the opposite side. Also if inequality does not contain an equality sign, then draw a dotted line.

Complete step by step solution:
To solve and graph the given inequality $ - x - 3 < - 5$, we will first
solve it for the value of $x$ as follows
$ \Rightarrow - x - 3 < - 5$
Adding $3$ both sides
$
\Rightarrow - x - 3 + 3 < - 5 + 3 \\
\Rightarrow - x < - 2 \\
$
Multiplying inequality with $ - 1$ to make coefficient of $x$ positive
$
\Rightarrow - 1 \times ( - x) < - 1 \times ( - 2) \\
\Rightarrow x > 2 \\
$
We get the required solution, expressing it in interval form, we will get
$x \in (2,\;\infty )$
Now, writing the inequality after as normal equation in order to plot its graph
$ \Rightarrow x = 2$
If we plot it in a Cartesian plane, we know that $x = a$ gives a line parallel to y-axis passing from point $(a,\;0)$
So graph of $x = 2$ will be drawn as follows

Now, coming to inequality $x > 2$
Checking it for point $(0,\;0)$
$ \Rightarrow 0 > 2$
$(0,\;0)$ does not holds good for the inequality, therefore we will shade its opposite side and also the inequality say $x$ should not equals to $2$ so we will draw dotted line

This is the required graph for the given inequality.

Note: Inequality sign inverted when we have multiplied $ - 1$ to the equation, let us understand it with example the inequality $6 > 5$ but when we multiply it with $ - 1$ that is $ - 1 \times 6 < - 1 \times 5 \Rightarrow - 6 < - 5$ the inequality sign gets inverted.