Respuesta :

Answer:

False

Step-by-step explanation:

3x2 is 6 and 6 +4 is not 0 it is ten 10 norder of operations

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                Hi my lil bunny!

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Lets do this step by step.

Simplify [tex]\frac{3x - 2}{x} -4[/tex].

To write -4 as a fraction with a common denominator, multiply by [tex]\frac{x}{x}[/tex]

[tex]\frac{3x - 2}{x} - 4 . \frac{x}{x} > 0[/tex]

Combine  -4 and [tex]\frac{x}{x}[/tex].

[tex]\frac{3x - 2}{x} + \frac{-4x}{x} > 0[/tex]

Combine the numerators over the common denominator.

[tex]\frac{3x - 2 -4x}{x} > 0[/tex]

Subtract 4x from 3x.

[tex]\frac{-x -2}{x} > 0[/tex]

Factor -1 out of -x.

[tex]\frac{-(-x) -2}{x} >0[/tex]

Rewirte -2 as -1 (2).

[tex]\frac{-(x -1 (2)}{x} > 0[/tex]

Factor -1 out of - (x) - 1 (2).

[tex]\frac{-(x + 2)}{x} >0[/tex]

Simplify the Expression.

_______________

Rewrite - ( x + 2 ) as -1 ( x + 2 ) .

[tex]\frac{-1 ( x+ 2)}{x} > 0[/tex]

Move the negative in front of the fraction.

[tex]- \frac{x + 2}{x} > 0[/tex]

Then your going to find all the values where the expression switches from negative to positive by setting each factor equal to 0  and solving.

[tex]x = 0\\x + 2 = 0[/tex]

Subtract 2 from both sides of the equation.

[tex]x = -2[/tex]

Solve for each factor to find the values where the absolute value expression goes from negative to positive.

[tex]x = 0 \\x = -2[/tex]

Consolidate the solutions.

[tex]x = 0, -2[/tex]

________________

Find the domain of [tex]\frac{3x - 2}{x} -4[/tex]

_________________

Set the denominator in [tex]\frac{3x - 2}{x}[/tex]  equal to 0 to find where the expression is undefined.

[tex]x = 0[/tex]

The domain is all values of x that make the expression defined.

( - ∞, 0 ) ∪ ( 0 , ∞)

Use each root to create test intervals.

[tex]x < -2 \\-2 < x < 0 \\x > 0[/tex]

|Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.|

Test a value on the interval -2 < x < 0 to see if it makes the inequality true.

Ans : True

Test a value on the interval x > 0 to see if it makes the inequality true.

Ans : False

Test a value on the interval x < -2  to see if it makes the inequality true.

Ans : False

Compare the intervals to determine which ones satisfy the original inequality.

[tex]x < -2 = False\\-2 < x < 0 = True\\x > 0 = False[/tex]

The solution consists of all of the true intervals.

[tex]-2 < x < 0[/tex]

The result can be shown in multiple forms.

Inequality Form: [tex]-2 < x< 0[/tex]

Interval Notation: [tex]( -2 , 0 )[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

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