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# How do you solve the inequality $- 5x \geqslant 25$?

Last updated date: 27th Feb 2024
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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.