Question
Solve the inequality and represent the solution graphically on number line: 2 (x – 1) < x + 5, 3 (x + 2) > 2 – x
✓
Answer
We have 2(x - 1) < x + 5, and 3(x + 2) > 2 - x
$ \Rightarrow 2x - 2 < x + 5$ and 3x + 6 > 2 - x
$ \Rightarrow x < 7$ and 4x > -4
$ \Rightarrow x < 7$ and x > -1
$ \Rightarrow 2x - 2 < x + 5$ and 3x + 6 > 2 - x
$ \Rightarrow x < 7$ and 4x > -4
$ \Rightarrow x < 7$ and x > -1
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Solve the inequality and show the graph for the solution on number line: 5x – 3 $\ge$ 3x – 5
→A big contains 6 red, 4 white and 8 blue balls, if three balls are drawn at random, find the probability that one is red, one is white and one is blue.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if:
- They can be of any colour.
- Two must be white and two red and.
- They must all be of the same colour.
Check the validity of the following statement.
q : 131 is a multiple of 3 or 11.
q : 131 is a multiple of 3 or 11.
Let R be the set of real numbers. Define the real function f: R $\rightarrow$ R by f(x) = x + 10 and sketch the graph of this function.
→Find k such that $\text{k}+9,\text{k}-6$ and 4 from three consecutive terms of a G.P.
→Write the following relation as the sets of ordered pairs:
A relation R on the set {1, 2, 3, 4, 5, 6, 7}defined by $(\text{x, y})\in \text{R}\Leftrightarrow\text{x}$ is relatively prime to y.
→A relation R on the set {1, 2, 3, 4, 5, 6, 7}defined by $(\text{x, y})\in \text{R}\Leftrightarrow\text{x}$ is relatively prime to y.
Solve the inequality and represent the solution graphically on number line: 5 (2x – 7) – 3 (2x + 3) $\le$ 0 , 2x + 19 $\le$ 6x + 47.
→In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only?
A G.P. consists of an even number of terms. If the sum of all the terms is $5$ times the sum of terms occupying odd places, then find its common ratio.
→