Question

If x< -x < 4x +10 find the interval in which x lies

Answer 1

As per the data given in the above question.

We have to find the interval lies in x.

Given,

$x< -x < 4x +10$

Step-by-step explanation:

A linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality.Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'.

Now ,

$x< -x < 4x +10 \: \: \: \: \: \: \: ...(1)$

Add x to all side in the equation (1)

$x + x< -x + x< 4x +10 + x$

$2x<0< 5x +10$

$2x< 5x +10$

Subtract 2x on the both side,

$2x - 2x< 5x +10 - 2x$

$0< 3x +10$

Subtract by (-10) on both side

$0 - 10< 3x +10 - 10$

$- 10< 3x$

Divide by 3 on the both side ,we get

$\frac{ - 10}{3} < x$

Therefore,

$x \: € ( \frac{ - 10}{3} , infinity)$

x lies between greater than -10/3 upto positive infinity.

Project code #SPJ1

Answer 2

Answer:

The interval in which "x" lies is (-2, 0)

Step-by-step explanation:

Given,

x < -x < 4x + 10

If we consider x < -x, then we can clearly see that this is possible only if "x" is negative i.e. x < 0.....(1)

Now we consider

-x < 4x + 10

⇒ 5x + 10 > 0

⇒ 5x > -10

⇒ x > -2....(2)

Now from (1) and (2)

we get to see that the interval in which "x" lies is (-2, 0)

#SPJ1