Math, asked by Madhushri7182, 10 months ago

Find the value of inequality |x-1|-3x/x-4<=1/2

Answers

Answered by shivapandeypandey123
2

Step-by-step explanation:

How do you solve the inequality

1

x

+

1

>

3

x

2

?

Algebra Multi-Step Inequalities

2 Answers

Lotusbluete

Jan 19, 2016

x

<

5

2

×

or

×

1

<

x

<

2

Explanation:

First of all, note that your inequality is only defined if your denominators are not equal to zero:

x

+

1

0

x

1

x

2

0

x

2

Now, your next step would be to "get rid" of the fractions. This can be done if multiplying both sides of the inequality with

x

+

1

and

x

2

.

However, you need to be careful since if you multiply an inequality with a negative number, you must flip the inequality sign.

=========================================

Let's consider the different cases:

case 1:

×

x

x

>

2

:

Both

x

+

1

>

0

and

x

2

>

0

hold. Thus, you get:

x

2

>

3

(

x

+

1

)

x

2

>

3

x

+

3

... compute

3

x

and

+

2

on both sides...

2

x

>

5

... divide by

2

on both sides. As

2

is a negative number, you must flip the inequality sign...

x

<

5

2

However, there is no

x

that satisfies both the condition

x

>

2

and

x

<

5

2

. Thus, there is no solution in this case.

=========================================

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