Advertisements
Advertisements
Question
x + 5 > 4x − 10
Solution
\[\text{ We have }, x + 5 > 4x - 10\]
\[ \Rightarrow 5 + 10 > 4x - x (\text{ Transposing x to the RHS and - 10 to the LHS })\]
\[ \Rightarrow 15 > 3x\]
\[ \Rightarrow 3x < 15\]
\[ \Rightarrow x < 5 \left( \text{ Dividing both sides by 3 } \right)\]
\[ \Rightarrow x \in \left( - \infty , 5 \right)\]
\[\text{ Hence, the solution set of the given inequation is } \left( - \infty , 5 \right) .\]
APPEARS IN
RELATED QUESTIONS
Solve: −4x > 30, when x ∈ R
Solve: −4x > 30, when x ∈ N
Solve: 4x − 2 < 8, when x ∈ R
Solve: 4x − 2 < 8, when x ∈ N
3x − 7 > x + 1
\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]
\[\frac{3}{x - 2} < 1\]
\[\frac{4x + 3}{2x - 5} < 6\]
\[\frac{x - 1}{x + 3} > 2\]
2x + 6 ≥ 0, 4x − 7 < 0
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.
3x − 1 ≥ 5, x + 2 > −1
Solve the following system of equation in R.
x + 5 > 2(x + 1), 2 − x < 3 (x + 2)
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
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
Solve \[\left| x + 1 \right| + \left| x \right| > 3\]
Write the solution set of the inequation
\[x + \frac{1}{x} \geq 2\]
Mark the correct alternative in each of the following:
If x and a are real numbers such that a\[>\]0 and \\left| x \right|\]\[>\]a, 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:
The inequality representing the following graph is
Mark the correct alternative in each of the following:
The solution set of the inequation \[\left| x + 2 \right|\]\[\leq\]5 is
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 natural number.
If |x + 3| ≥ 10, then ______.
If a < b and c < 0, then `a/c` ______ `b/c`.
If |x − 1| ≤ 2, then –1 ______ x ______ 3
Solve for x, the inequality given below.
`1/(|x| - 3) ≤ 1/2`
A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?
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 − 1| > 5, then ______.
If |x + 2| ≤ 9, then ______.
If x < –5 and x > 2, then x ∈ (– 5, 2)
If x > – 5, then 4x ______ –20.
If p > 0 and q < 0, then p – q ______ p.
