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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.

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