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3 years ago

Solve this inequality 5 x + 2 < 32

Mathematics

1 answer:

Hatshy [7]3 years ago

7 0

Answer:

Here is your answer:

5x + 2 < 32

solution:

5x+ 2 < 32

or, 5x < 32-2

or, 5x < 30

or, 5x < 30/2

or, 5x < 15

or, x < 15/3

or, x < 5

therefore, x < 5 ans

Hope it will help you

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Answer: The required values are $\dfrac{169}{4}~~\textup{and}~~\dfrac{157}{4}.$

Step-by-step explanation: The given quadratic equation is

$x^2+13x=-3~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the values that make an equivalent number sentence after completing the square.

COMPLETING THE SQUARE : Its a method of making one side of a quadratic equation a perfect square, so that the equation can be solved easily by taking the square root on both the sides of the equation.

From equation (i), we have

$x^2+13x=-3\\\\\Rightarrow x^2+2\times x\times \dfrac{13}{2}+\left(\dfrac{13}{2}\right)^2=\left(\dfrac{13}{2}\right)^2-3\\\\\\\Rightarrow \left(x+\dfrac{13}{2}\right)^2=\dfrac{169}{4}-3\\\\\\\Rightarrow \left(x+\dfrac{13}{2}\right)^2=\dfrac{157}{4}.$

So, the complete statement is

$x^2+13x+\dfrac{169}{4}=\dfrac{157}{4}.$

Thus, the required values are $\dfrac{169}{4}~~\textup{and}~~\dfrac{157}{4}.$

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