Advertisements
Advertisements
प्रश्न
Solve each of the following system of equations in R.
2x + 5 ≤ 0, x − 3 ≤ 0
उत्तर
\[\text{ We have }, 2x + 5 \leq 0\]
\[ \Rightarrow 2x \leq - 5\]
\[ \Rightarrow x \leq \frac{- 5}{2}\]
\[ \Rightarrow x \in ( - \infty , \frac{- 5}{2}] . . . (i)\]
\[\text{ Also }, x - 3 \leq 0\]
\[ \Rightarrow x \leq 3\]
\[ \Rightarrow x \in ( - \infty , 3] . . . (ii)\]
\[\text{ Thus, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) . \]
\[( - \infty , \frac{- 5}{2}] \cap ( - \infty , 3] = ( - \infty , \frac{- 5}{2}]\]
\[\text{ Thus, the solution of the given set of inequalities is } ( - \infty , \frac{- 5}{2}] . \]
\[\]
APPEARS IN
संबंधित प्रश्न
Solve: −4x > 30, when x ∈ N
\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]
\[\frac{2x - 3}{3x - 7} > 0\]
\[\frac{3}{x - 2} < 1\]
\[\frac{1}{x - 1} \leq 2\]
\[\frac{x}{x - 5} > \frac{1}{2}\]
Solve each of the following system of equations in R.
x − 2 > 0, 3x < 18
2x + 6 ≥ 0, 4x − 7 < 0
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
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve
\[\left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}\]
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\left| 3 - 4x \right| \geq 9\]
Write the solution set of the inequation
\[x + \frac{1}{x} \geq 2\]
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 \[\left| x + 2 \right|\]\[\leq\]9, then
Mark the correct alternative in each of the following:
The linear inequality representing the solution set given in 
Solve the inequality, 3x – 5 < x + 7, when x is an integer.
Solve |3 – 4x| ≥ 9.
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?
The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then ______.
If |x − 1| ≤ 2, then –1 ______ x ______ 3
If p > 0 and q < 0, then p + q ______ p.
Solve for x, the inequality given below.
`4/(x + 1) ≤ 3 ≤ 6/(x + 1)`, (x > 0)
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
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.
If x is a real number and |x| < 3, then ______.
x and b are real numbers. If b > 0 and |x| > b, then ______.
If |x + 2| ≤ 9, then ______.
If x < –5 and x > 2, then x ∈ (– 5, 2)
If `2/(x + 2) > 0`, then x ______ –2.
If x > – 5, then 4x ______ –20.
If p > 0 and q < 0, then p – q ______ p.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.
If – 2x + 1 ≥ 9, then x ______ – 4.
