Question

Find the following solution of inequality $ x - 5 \geqslant - 7 $, also show it graphically.

Answer 1

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.