###### Advertisements

###### Advertisements

\[\frac{6x - 5}{4x + 1} < 0\]

###### Advertisements

#### Solution

\[\frac{6x - 5}{4x + 1} < 0\]

\[\text{ Equating } 6x - 5 \text{ and } 4x + 1 \text{ to zero, we obtain } x = \frac{5}{6} \text{ and } - \frac{1}{4} \text{ as the critical points } . \]

\[\therefore x \in \left( \frac{- 1}{4}, \frac{5}{6} \right)\]

\[\]

#### APPEARS IN

#### RELATED QUESTIONS

*x* + 5 > 4*x* − 10

\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]

\[\frac{x - 1}{3} + 4 < \frac{x - 5}{5} - 2\]

\[\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2\]

\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]

\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]

\[\frac{1}{x - 1} \leq 2\]

\[\frac{5x + 8}{4 - x} < 2\]

Solve each of the following system of equations in R.

*x* − 2 > 0, 3*x* < 18

2*x* + 6 ≥ 0, 4*x* − 7 < 0

Solve each of the following system of equations in R.

3*x* − 6 > 0, 2*x* − 5 > 0

Solve each of the following system of equations in R.

4*x* − 1 ≤ 0, 3 − 4*x* < 0

Solve each of the following system of equations in R.

\[\frac{7x - 1}{2} < - 3, \frac{3x + 8}{5} + 11 < 0\]

Solve each of the following system of equations in R.

\[0 < \frac{- x}{2} < 3\]

Solve each of the following system of equations in R.

10 ≤ −5 (*x* − 2) < 20

Solve each of the following system of equations in R.

20. −5 < 2*x* − 3 < 5

Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]

Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]

Mark the correct alternative in each of the following:

The inequality representing the following graph is

Mark the correct alternative in each of the following:

The linear inequality representing the solution set given in

Mark the correct alternative in each of the following:

If \[\frac{\left| x - 2 \right|}{x - 2}\]\[\geq\] then

Solve the inequality, 3x – 5 < x + 7, when x is an integer.

Solve the inequality, 3x – 5 < x + 7, when x is a real number.

The cost and revenue functions of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?

Solve for x, `(|x + 3| + x)/(x + 2) > 1`.

If x ≥ –3, then x + 5 ______ 2.

If –x ≤ –4, then 2x ______ 8.

If a < b and c < 0, then `a/c` ______ `b/c`.

If |3x – 7| > 2, then x ______ `5/3` or x ______ 3.

Solve for x, the inequality given below.

`4/(x + 1) ≤ 3 ≤ 6/(x + 1)`, (x > 0)

State which of the following statement is True or False.

If x < –5 and x < –2, then x ∈ (–∞, –5)

If x > – 5, then 4x ______ –20.

If p > 0 and q < 0, then p – q ______ p.

If |x + 2| > 5, then x ______ – 7 or x ______ 3.