Advertisements
Advertisements
प्रश्न
\[\frac{x}{5} < \frac{3x - 2}{4} - \frac{5x - 3}{5}\]
उत्तर
\[\frac{x}{5} < \frac{3x - 2}{4} - \frac{5x - 3}{5}\]
\[ \Rightarrow 20 \times \left( \frac{x}{5} \right) < 20 \times \left( \frac{3x - 2}{4} - \frac{5x - 3}{5} \right) \left( \text{ Multiplying both the sides by 20 } \right)\]
\[ \Rightarrow 4x < 5\left( 3x - 2 \right) - 4\left( 5x - 3 \right)\]
\[ \Rightarrow 4x < 15x - 10 - 20x + 12\]
\[ \Rightarrow 4x < - 5x + 2\]
\[ \Rightarrow 4x + 5x < 2 (\text{ Transposing - 5x to the LHS) } \]
\[ \Rightarrow 9x < 2\]
\[ \Rightarrow x < \frac{2}{9} (\text{ Dividing both the sides by 9 }) \hspace{0.167em} \]
\[\text{ Hence, the solution set of the given inequation is } \left( - \infty , \frac{2}{9} \right) .\]
APPEARS IN
संबंधित प्रश्न
Solve: −4x > 30, when x ∈ R
Solve: −4x > 30, when x ∈ N
3x + 9 ≥ −x + 19
\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]
\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]
\[x - 2 \leq \frac{5x + 8}{3}\]
\[\frac{x - 1}{x + 3} > 2\]
\[\frac{7x - 5}{8x + 3} > 4\]
Solve each of the following system of equations in R.
1. x + 3 > 0, 2x < 14
Solve each of the following system of equations in R.
x − 2 > 0, 3x < 18
Solve each of the following system of equations in R.
5x − 1 < 24, 5x + 1 > −24
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 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.
\[0 < \frac{- x}{2} < 3\]
Solve each of the following system of equations in R.
20. −5 < 2x − 3 < 5
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
Solve \[\left| x + 1 \right| + \left| x \right| > 3\]
Solve \[\left| 3 - 4x \right| \geq 9\]
Mark the correct alternative in each of the following:
If \[\left| x + 3 \right|\]\[\geq\]10, then
Solve the inequality, 3x – 5 < x + 7, when x is a whole number.
Solve the inequality, 3x – 5 < x + 7, when x is an integer.
Solve |3 – 4x| ≥ 9.
Solve for x, `(|x + 3| + x)/(x + 2) > 1`.
If `|x - 2|/(x - 2) ≥ 0`, then ______.
If x ≥ –3, then x + 5 ______ 2.
If –x ≤ –4, then 2x ______ 8.
If `1/(x - 2) < 0`, then x ______ 2.
If a < b and c < 0, then `a/c` ______ `b/c`.
A solution is to be kept between 40°C and 45°C. What is the range of temperature in degree fahrenheit, if the conversion formula is F = `9/5` C + 32?
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 – 4x ≥ 12, then x ______ – 3.
If p > 0 and q < 0, then p – q ______ p.
