Advertisements
Advertisements
प्रश्न
Solve each of the following system of equations in R.
11 − 5x > −4, 4x + 13 ≤ −11
उत्तर
We have,
\[11 - 5x > - 4\]
\[ \Rightarrow - 5x > - 4 - 11\]
\[ \Rightarrow - 5x > - 15\]
\[ \Rightarrow 5x < 15 \left[ \text{ Multiplying both sides by }- 1 \right]\]
\[ \Rightarrow x < \frac{15}{5} \]
\[ \Rightarrow x < 3\]
\[ \Rightarrow x \in ( - \infty , 3) . . . (i)\]
\[\text{ Also }, 4x + 13 \leq - 11\]
\[ \Rightarrow 4x \leq - 11 - 13\]
\[ \Rightarrow 4x \leq - 24\]
\[ \Rightarrow x \leq - 6\]
\[ \Rightarrow x \in ( - \infty , - 6] . . . (ii)\]
\[\text{ Hence, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) . \]
\[( - \infty 3) \cap ( - \infty , - 6] = ( - \infty , - 6]\]
\[\text{ Hence, the solution of the given set of inequalities is } ( - \infty , - 6] .\]
APPEARS IN
संबंधित प्रश्न
Solve: 12x < 50, when x ∈ R
Solve: 4x − 2 < 8, when x ∈ N
x + 5 > 4x − 10
\[2\left( 3 - x \right) \geq \frac{x}{5} + 4\]
−(x − 3) + 4 < 5 − 2x
\[\frac{5x}{2} + \frac{3x}{4} \geq \frac{39}{4}\]
\[\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2\]
\[\frac{3}{x - 2} < 1\]
\[\frac{5x - 6}{x + 6} < 1\]
\[\frac{x - 1}{x + 3} > 2\]
\[\frac{7x - 5}{8x + 3} > 4\]
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 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
\[\left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}\]
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 x is a real number and \[\left| x \right|\]\[<\]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:
If \[\frac{\left| x - 2 \right|}{x - 2}\]\[\geq\] then
The cost and revenue functions of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?
Solve for x, |x + 1| + |x| > 3.
Solve for x, the inequality given below.
`(|x - 2| - 1)/(|x - 2| - 2) ≤ 0`
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?
The water acidity in a pool is considerd normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the first two pH readings are 8.48 and 8.35, find the range of pH value for the third reading that will result in the acidity level being normal.
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 – 4x ≥ 12, then x ______ – 3.
If x > y and z < 0, then – xz ______ – yz.
If p > 0 and q < 0, then p – q ______ p.
If – 2x + 1 ≥ 9, then x ______ – 4.
