Advertisements
Advertisements
Question
Solve: 12x < 50, when x ∈ R
Solution
\[\text{ We have }, 12x < 50\]
\[ \Rightarrow x < \frac{50}{12} \left[ \text{ Dividing both the sides by } 12 \right]\]
\[ \Rightarrow x < \frac{25}{6}\]
\[ x \in R\]
\[\text{ Then, the solution of the given inequation is } \left( - \infty , \frac{25}{6} \right) . \]
APPEARS IN
RELATED QUESTIONS
Solve: −4x > 30, when x ∈ R
Solve: 4x − 2 < 8, when x ∈ N
3x − 7 > x + 1
3x + 9 ≥ −x + 19
\[2\left( 3 - x \right) \geq \frac{x}{5} + 4\]
−(x − 3) + 4 < 5 − 2x
\[\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2\]
\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]
\[\frac{2x + 3}{5} - 2 < \frac{3\left( x - 2 \right)}{5}\]
\[x - 2 \leq \frac{5x + 8}{3}\]
\[\frac{4x + 3}{2x - 5} < 6\]
\[\frac{5x - 6}{x + 6} < 1\]
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.
2x − 3 < 7, 2x > −4
Solve each of the following system of equations in R.
2x + 5 ≤ 0, x − 3 ≤ 0
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.
\[\frac{2x - 3}{4} - 2 \geq \frac{4x}{3} - 6, 2\left( 2x + 3 \right) < 6\left( x - 2 \right) + 10\]
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.
20. −5 < 2x − 3 < 5
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\left| x - 1 \right| + \left| x - 2 \right| + \left| x - 3 \right| \geq 6\]
Mark the correct alternative in each of the following:
If x is a real number and \[\left| x \right|\]\[<\]5, then
Mark the correct alternative in each of the following:
\[\left| x - 1 \right|\]\[>\]5, then
Mark the correct alternative in each of the following:
If \[\frac{\left| x - 2 \right|}{x - 2}\]\[\geq\] then
Solve |3 – 4x| ≥ 9.
Solve for x, `(|x + 3| + x)/(x + 2) > 1`.
Solve the following system of inequalities:
`x/(2x + 1) ≥ 1/4, (6x)/(4x - 1) < 1/2`
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.
In drilling world’s deepest hole it was found that the temperature T in degree celcius, x km below the earth’s surface was given by T = 30 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?
If x is a real number and |x| < 3, then ______.
If |x + 2| ≤ 9, then ______.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.