Advertisements
Advertisements
प्रश्न
\[\frac{x}{x - 5} > \frac{1}{2}\]
उत्तर
\[\frac{x}{x - 5} > \frac{1}{2}\]
\[ \Rightarrow \frac{x}{x - 5} - \frac{1}{2} > 0\]
\[ \Rightarrow \frac{2x - x + 5}{2(x - 5)} > 0\]
\[ \Rightarrow \frac{x + 5}{2(x - 5)} > 0\]
\[ \Rightarrow \frac{x + 5}{x - 5} > 0\]
\[\therefore x \in \left( - \infty , - 5 \right) \cup \left( 5, \infty \right)\]
APPEARS IN
संबंधित प्रश्न
Solve: 12x < 50, when x ∈ Z
Solve: −4x > 30, when x ∈ R
Solve: −4x > 30, when x ∈ Z
Solve: 4x − 2 < 8, when x ∈ R
3x − 7 > x + 1
\[\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2\]
\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]
\[x - 2 \leq \frac{5x + 8}{3}\]
\[\frac{1}{x - 1} \leq 2\]
Solve each of the following system of equations in R.
2x − 7 > 5 − x, 11 − 5x ≤ 1
Solve the following system of equation in R.
x + 5 > 2(x + 1), 2 − x < 3 (x + 2)
Solve the following system of equation in R.
\[\frac{2x + 1}{7x - 1} > 5, \frac{x + 7}{x - 8} > 2\]
Solve each of the following system of equations in R. \[\frac{4}{x + 1} \leq 3 \leq \frac{6}{x + 1}, x > 0\]
Solve
\[\left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}\]
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\frac{\left| x + 2 \right| - x}{x} < 2\]
Write the solution set of the inequation
\[x + \frac{1}{x} \geq 2\]
Mark the correct alternative in each of the following:
If − 3x\[+\]17\[< -\]13, then
Mark the correct alternative in each of the following:
The linear inequality representing the solution set given in 
Solve the inequality, 3x – 5 < x + 7, when x is a real number.
Solve |3 – 4x| ≥ 9.
Solve for x, |x + 1| + |x| > 3.
Solve the following system of inequalities:
`x/(2x + 1) ≥ 1/4, (6x)/(4x - 1) < 1/2`
If `|x - 2|/(x - 2) ≥ 0`, then ______.
If |x + 3| ≥ 10, then ______.
If `1/(x - 2) < 0`, then x ______ 2.
If |x − 1| ≤ 2, then –1 ______ x ______ 3
If p > 0 and q < 0, then p + q ______ p.
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
If x < 5, then ______.
If |x − 1| > 5, then ______.
State which of the following statement is True or False.
If xy < 0, then x < 0 and y < 0
If – 4x ≥ 12, then x ______ – 3.
If `2/(x + 2) > 0`, then x ______ –2.
If p > 0 and q < 0, then p – q ______ p.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.
