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