Answer

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**Hint:**An Inequality is a mathematical statement that compares two expressions using an inequality sign. In this inequality, one expression of the inequality can be greater or less than the other expression.

**Complete step by step solution:**

Given inequality is $ x - 5 \geqslant - 7 $

Isolate the variable by adding\[7\]to both sides of the inequality

$

\left( {x - 5} \right) + 7 \geqslant - 7 + 7 \\

(x - 5) + 7 \geqslant 0 \\

x + 2 \geqslant 0 \\

$

Now isolate the variable by adding\[ - 2\]to both sides of the inequality we get,

$

(x + 2) + ( - 2) \geqslant - 2 \\

x + 2 - 2 \geqslant - 2 \\

x \geqslant - 2 \\

\therefore x \in [ - 2,\infty ) \\

$

Which means values of x can go from point\[ - 2\]to positive side in an endless direction that is $ [ - 2,\infty ) $.

To represent it on a Graph:

Inequality can be represented on a number line. The point is\[ - 2,\]represented with a closed circle since the inequality is greater than or equal to\[ - 2.\]

The above line is drawn to the right on the number line because the values in this part of the number line are greater than -2. The arrow at the end indicates that the solutions continue till infinity.

**Note:**Solving inequality is similar to solving equations except we have to reverse the inequality symbols when we multiply or divide both sides of an inequality by a negative number. Since the inequality can have multiple solutions, it is customary to represent the solution in inequality graphically as well as algebraically.

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