Advertisements
Advertisements
प्रश्न
\[\frac{2\left( x - 1 \right)}{5} \leq \frac{3\left( 2 + x \right)}{7}\]
उत्तर
\[\frac{2\left( x - 1 \right)}{5} \leq \frac{3\left( 2 + x \right)}{7}\]
\[ \Rightarrow 14\left( x - 1 \right) \leq 15\left( 2 + x \right) \]
\[ \Rightarrow 14x - 14 \leq 30 + 15x\]
\[ \Rightarrow 30 + 15x \geq 14x - 14\]
\[ \Rightarrow 15x - 14x \geq - 14 - 30 (\text{ Transposing 14x to the LHS and 30 to the RHS })\]
\[ \Rightarrow x \geq - 44\]
\[\text{ Hence, the solution to the given inequation is } [ - 44, \infty ) .\]
APPEARS IN
संबंधित प्रश्न
Solve: 12x < 50, when x ∈ N
Solve: −4x > 30, when x ∈ Z
Solve: 4x − 2 < 8, when x ∈ R
Solve: 4x − 2 < 8, when x ∈ Z
−(x − 3) + 4 < 5 − 2x
\[\frac{5x}{2} + \frac{3x}{4} \geq \frac{39}{4}\]
\[x - 2 \leq \frac{5x + 8}{3}\]
\[\frac{6x - 5}{4x + 1} < 0\]
Solve each of the following system of equations in R.
2x − 7 > 5 − x, 11 − 5x ≤ 1
2x + 6 ≥ 0, 4x − 7 < 0
Solve the following system of equation in R.
x + 5 > 2(x + 1), 2 − x < 3 (x + 2)
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve
\[\left| \frac{2x - 1}{x - 1} \right| > 2\]
Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]
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:
Given that x, y and b are real numbers and x\[<\]y, b\[>\]0, then
Mark the correct alternative in each of the following:
The linear inequality representing the solution set given in 
Mark the correct alternative in each of the following:
The solution set of the inequation \[\left| x + 2 \right|\]\[\leq\]5 is
Solve the inequality, 3x – 5 < x + 7, when x is a real number.
Solve 1 ≤ |x – 2| ≤ 3.
Solve for x, `(|x + 3| + x)/(x + 2) > 1`.
If `|x - 2|/(x - 2) ≥ 0`, then ______.
If |x + 3| ≥ 10, then ______.
If –x ≤ –4, then 2x ______ 8.
If a < b and c < 0, then `a/c` ______ `b/c`.
Solve for x, the inequality given below.
`1/(|x| - 3) ≤ 1/2`
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?
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?
If x < 5, then ______.
Given that x, y and b are real numbers and x < y, b < 0, then ______.
If x is a real number and |x| < 3, then ______.
State which of the following statement is True or False.
If x < –5 and x < –2, then x ∈ (–∞, –5)
If – 4x ≥ 12, then x ______ – 3.
If – 2x + 1 ≥ 9, then x ______ – 4.
