Question

How do you solve the inequality \[ - 5x \geqslant 25\]?

Answer 1

Hint: An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Here we need to solve for ‘x’ which is a variable. Solving the given inequality is very like solving equations and we do most of the same thing but we must pay attention to the direction of inequality\[( \leqslant , > )\].

Complete step-by-step solution:
Given, \[ - 5x \geqslant 25\].
Now we need to solve for ‘x’.
Since we have negative 5 on the left hand side. If we divide a negative number on both side the inequality the sign changes.
Now divide -5 on both side of the inequality we have,
 \[
  x \leqslant \dfrac{{25}}{{ - 5}} \\
  x \leqslant - 5 \\
 \]
Thus the solution of \[ - 5x \geqslant 25\] is \[x \leqslant - 5\].
In interval form we have \[( - \infty ,5]\].
(If we have \[ \leqslant or \geqslant \] we use closed intervals. If we have \[ > or < \] we use open interval)

Note: We know that \[a \ne b\]is says that ‘a’ is not equal to ‘b’. \[a > b\] means that ‘a’ is less than ‘b’. \[a < b\] means that ‘a’ is greater than ‘b’. These two are known as strict inequality. \[a \geqslant b\] means that ‘a’ is less than or equal to ‘b’. \[a \leqslant b\] means that ‘a’ is greater than or equal to ‘b’.

The direction of inequality do not change in these cases:
-Add or subtract a number from both sides.
-Multiply or divide both sides by a positive number.
-Simplify a side.

The direction of the inequality change in these cases:
-Multiply or divide both sides by a negative number.
-Swapping left and right hand sides.