Answer
Linear inequalities is the same as the producers for the solving linear equation. The sense of the linear inequality changes when we multiply by a negative number on both sides. The multiplication and division on both sides of the linear inequalities by a negative number change the senses of it.
Work Step by Step
Solving an inequality is the process of finding the set of numbers that makes the inequality a true statement.
The procedure for solving linear inequalities is the same as the procedure for solving linear equations, with one important exception. When multiplying or dividing both sides of the inequalities by a negative number, reverse the direction of the inequality symbol, changing the sense of the inequality.
For example:
\[-\frac{1}{4}x\ge 8\]
\[\text{Multiplying both sides by -4}\], we get
\[\text{x}\le \text{-32}\]
So, the sense of the linear inequality changes when we multiply by a negative number on both sides.
Hence, the multiplication and division on both sides of the linear inequalities by a negative number changes the sense of it.
