\[\begin{array}{*{35}{l}} P\text{ }=\text{ }\{x:\text{ }7x\text{ }\text{ }2\text{ }>\text{ }4x\text{ }+\text{ }1,\text{ }x\in R\} \\ 7x\text{ }\text{ }2\text{ }>\text{ }4x\text{ }+\text{ }1 ...
P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 ≥ 5(x – 5); where x ∈ R. Represent: (i) P ∩ Q (ii) P – Q
\[P\text{ }=\text{ }\{x:\text{ }7x\text{ }\text{ }2\text{ }>\text{ }4x\text{ }+\text{ }1,\text{ }x\in R\}\] \[\begin{array}{*{35}{l}} 7x\text{ }\text{ }2\text{ }>\text{ }4x\text{ }+\text{ }1 ...
Given A = {x: -1 < x ≤ 5, x ∈ R} and B = {x: -4 ≤ x < 3, x ∈ R} Represent on different number lines: A – B
\[~A\text{ }\text{ }B\text{ }=\text{ }\left\{ x:\text{ }3\text{ }\le \text{ }x\text{ }\le \text{ }5,\text{ }x\in R \right\}\] Also, it very well may be addressed on a number line as:
Given A = {x: -1 < x ≤ 5, x ∈ R} and B = {x: -4 ≤ x < 3, x ∈ R} Represent on different number lines: (i) A ∩ B (ii) A’ ∩ B
(I) \[A\text{ }\cap \text{ }B\text{ }=\text{ }\{x:\text{ }-\text{ }1\text{ }<\text{ }x\text{ }<\text{ }3,\text{ }x\in R\}\] Also, it very well may be addressed on a number line as: (ii)...
Illustrate the set {x: -3 ≤ x 2, x ∈ R} on the real number line.
We need to get that: Diagram of arrangement set of \[-\text{ }3\text{ }\le \text{ }x\text{ }<\text{ }0\text{ }or\text{ }x\text{ }>\text{ }2\text{ }=\]Graph of focuses which have a place with...
Use real number line to find the range of values of x for which: -1 < x ≤ 6 and -2 ≤ x ≤ 3
\[-\text{ }1\text{ }<\text{ }x\text{ }\le \text{ }6\text{ }and\text{ }-\text{ }2\text{ }\le \text{ }x\text{ }\le \text{ }3\] Both the given inequations are valid in the reach where their charts...
Use real number line to find the range of values of x for which: (i) x > 3 and 0 < x < 6 (ii) x < 0 and -3 ≤ x < 1
(I) \[x\text{ }>\text{ }3\text{ }and\text{ }0\text{ }<\text{ }x\text{ }<\text{ }6\] Both the given inequations are valid in the reach where their charts on the genuine number lines...
The diagram represents two inequations A and B on real number lines: (i) Write down A and B in set builder notation. (ii) Represent A ∩ B and A ∩ B’ on two different number lines.
SOLUTION:- (I) \[A\text{ }=\text{ }\{x\in R:\text{ }-\text{ }2\le x\text{ }<\text{ }5\}\] \[B\text{ }=\text{ }\left\{ x\in R:\text{ }-\text{ }4\le x\text{ }<\text{ }3 \right\}\] (ii) \[A\text{...
Solve and graph the solution set of: (i) 3x – 2 > 19 or 3 – 2x ≥ -7, x ∈ R (ii) 5 > p – 1 > 2 or 7 ≤ 2p – ≤ 17, p ∈ R
(I) \[3x\text{ }\text{ }2\text{ }>\text{ }19\text{ }or\text{ }3\text{ }\text{ }2x\text{ }\ge \text{ }-\text{ }7\] \[\begin{array}{*{35}{l}} 3x\text{ }>\text{ }21\text{ }or\text{ }-\text{...
Solve and graph the solution set of: x + 5 ≥ 4(x – 1) and 3 – 2x < -7, x ∈ R
\[\begin{align} & ~x\text{ }+\text{ }5\text{ }\ge \text{ }4\left( x\text{ }\text{ }1 \right)\text{ }and\text{ }3\text{ }\text{ }2x\text{ }<\text{ }-\text{ }7 \\ & \begin{array}{*{35}{l}}...
Solve and graph the solution set of: (i) 2x – 9 25, x ∈ I
(I) \[2x\text{ }\text{ }9\text{ }<\text{ }7\text{ }and\text{ }3x\text{ }+\text{ }9\text{ }\le \text{ }25\] \[\begin{array}{*{35}{l}} 2x\text{ }<\text{ }16\text{ }and\text{ }3x\text{ }\le...
Solve the following inequation and graph the solution set on the number line: 2x – 3 < x + 2 ≤ 3x + 5, x ∈ R.
Given inequation, \[\begin{align} & \begin{array}{*{35}{l}} 2x\text{ }\text{ }3\text{ }<\text{ }x\text{ }+\text{ }2\text{ }\le \text{ }3x\text{ }+\text{ }5 \\ 2x\text{ }\text{ }3\text{...
If 5x – 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.
Given inequation, \[\begin{array}{*{35}{l}} 5x\text{ }\text{ }3\text{ }\le \text{ }5\text{ }+\text{ }3x\text{ }\le \text{ }4x\text{ }+\text{ }2 \\ 5x\text{ }\text{ }3\text{ }\le \text{ }5\text{...
Given x ∈ {real numbers}, find the range of values of x for which -5 ≤ 2x – 3 < x + 2 and represent it on a real number line.
Given inequation, \[\begin{array}{*{35}{l}} -\text{ }5\text{ }\le \text{ }2x\text{ }\text{ }3\text{ }<\text{ }x\text{ }+\text{ }2 \\ -\text{ }5\text{ }\le \text{ }2x\text{ }\text{ }3\text{...
Find the values of x, which satisfy the inequation:
Graph the solution on the number line. SOLUTION:- Given Inequation, Henceforth, the arrangement set is \[\{x\in N:\text{ }-\text{ }2\le x\le 3.75\}\] Also, as x ∈ N, the upsides of x are \[1,\text{...
Find the range of values of x which satisfies
Graph these values of x on the number line. SOLUTION:- \[\Rightarrow -\text{ }3\le x\text{ }and\text{ }x\text{ }<\text{ }3\] Along these lines, \[3\text{ }\le \text{ }x\text{ }<\text{ }3\]...
List the elements of the solution set of the inequation -3 < x – 2 ≤ 9 – 2x; x ∈ N.
\[-\text{ }3\text{ }<\text{ }x\text{ }\text{ }2\text{ }\le \text{ }9\text{ }\text{ }2x\] \[\begin{array}{*{35}{l}} -\text{ }3\text{ }<\text{ }x\text{ }\text{ }2\text{ }and\text{ }x\text{...
x ∈ {real numbers} and -1 < 3 – 2x ≤ 7, evaluate x and represent it on a number line.
\[\begin{array}{*{35}{l}} -\text{ }1\text{ }<\text{ }3\text{ }\text{ }2x\text{ }\le \text{ }7 \\ -\text{ }1\text{ }<\text{ }3\text{ }\text{ }2x\text{ }and\text{ }3\text{ }\text{ }2x\text{...
Represent the solution of each of the following inequations on the real number line: (i)1 + x ≥ 5x – 11 (ii) (2x + 5)/3 > 3x – 3
(i) \[1\text{ }+\text{ }x\text{ }\ge \text{ }5x\text{ }\text{ }11\] \[\begin{array}{*{35}{l}} 12\text{ }\ge \text{ }4x \\ x\text{ }\le \text{ }3 \\ \end{array}\] The arrangement on number line is...
Represent the solution of each of the following inequations on the real number line: (i)x + 3 ≤ 2x + 9 (ii) 2 – 3x > 7 – 5x
(i) \[x\text{ }+\text{ }3\text{ }\le \text{ }2x\text{ }+\text{ }9\] \[\begin{array}{*{35}{l}} x\text{ }\text{ }2x\text{ }\le \text{ }-\text{ }3\text{ }+\text{ }9 \\ -\text{ }x\text{ }\le \text{ }6 ...
Represent the solution of each of the following inequations on the real number line: (i) 4x – 1 > x + 11 (ii) 7 – x ≤ 2 – 6x
(I) \[4x\text{ }\text{ }1\text{ }>\text{ }x\text{ }+\text{ }11\] \[\begin{array}{*{35}{l}} 4x\text{ }\text{ }x\text{ }>\text{ }1\text{ }+\text{ }11 \\ 3x\text{ }>\text{ }12 \\ x\text{...
For the following inequation, graph the solution set on the real number line: (i) -4 ≤ 3x – 1 < 8 (ii) x -1 < 3- x ≤ 5
(I) \[-\text{ }4\text{ }\le \text{ }3x\text{ }\text{ }1\text{ }<\text{ }8\] \[\begin{array}{*{35}{l}} -\text{ }4\text{ }\le \text{ }3x\text{ }\text{ }1\text{ }and\text{ }3x\text{ }\text{ }1\text{...
For each graph given alongside, write an inequation taking x as the variable:
(i) (ii) Solution:- (i) \[-4\text{ }\le \text{ }x\text{ }<\text{ }3,\text{ }x\in R\] (ii) \[-1\text{ }<\text{ }x\text{ }\le \text{ }5,\text{ }x\in R\]
For each graph given alongside, write an inequation taking x as the variable:
(i) (ii) Solution:- (i) \[x\text{ }\le \text{ }1,\text{ }x\in R\] (ii) \[x\text{ }\ge \text{ }2,\text{ }x\in R\]
Represent the following inequalities on real number line: -5 < x ≤ -1
\[-\text{ }5\text{ }<\text{ }x\text{ }\le \text{ }-\text{ }1\] Arrangement on the number line is as beneath
Represent the following inequalities on real number line: (i) -2 ≤ x -3
(i) \[-\text{ }2\text{ }\le \text{ }x\text{ }<\text{ }5\] Arrangement on the number line is as beneath (ii) \[8\text{ }\ge \text{ }x\text{ }>\text{ }-\text{ }3\] Arrangement on the...
Represent the following inequalities on real number line: (i) 2(2x – 3) ≤ 6 (ii) -4 < x < 4
(i) \[2\left( 2x\text{ }\text{ }3 \right)\text{ }\le \text{ }6\] \[\begin{array}{*{35}{l}} 4x\text{ }\text{ }6\text{ }\le \text{ }6 \\ 4x\text{ }\le \text{ }12 \\ x\text{ }\le \text{ }3 \\...
Represent the following inequalities on real number line: (i) 2x – 1 < 5 (ii) 3x + 1 ≥ -5
(I) \[2x\text{ }\text{ }1\text{ }<\text{ }5\] \[\begin{array}{*{35}{l}} 2x\text{ }<\text{ }6 \\ x\text{ }<\text{ }3 \\ \end{array}\] Arrangement on the number line is as beneath ...