Answer

Verified

380.7k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How many crores make 10 million class 7 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths