2x – 7 > 5 – x and 11 – 5x ≤ 1 Let us consider the first inequality. \[\begin{array}{*{35}{l}} 2x\text{ }-\text{ }7\text{ }>\text{ }5\text{ }-\text{ }x \\ 2x\text{ }-\text{ }7\text{ }+\text{...
x + 3 > 0 and 2x < 14 Let us consider the first inequality. \[\begin{array}{*{35}{l}} x\text{ }+\text{ }3\text{ }>\text{ }0 \\ x\text{ }+\text{ }3\text{ }-\text{ }3\text{ }>\text{...
\[\begin{array}{*{35}{l}} \left( 2x\text{ }+\text{ }3 \right)/4\text{ }-\text{ }3\text{ }<\text{ }\left( x\text{ }-\text{ }4 \right)/3\text{ }-\text{ }2 \\ \left( 2x\text{ }+\text{ }3...
\[\begin{array}{*{35}{l}} \left( x\text{ }-\text{ }1 \right)/3\text{ }+\text{ }4\text{ }<\text{ }\left( x\text{ }-\text{ }5 \right)/5\text{ }-\text{ }2 \\ Subtract\text{ }both\text{ }sides\text{...
\[\begin{array}{*{35}{l}} 5x/2\text{ }+\text{ }3x/4\text{ }\ge \text{ }39/4 \\ taking\text{ }LCM \\ \left[ 2\left( 5x \right)+3x \right]/4\text{ }\ge \text{ }39/4 \\ 13x/4\text{ }\ge \text{...
\[2\left( x-1 \right)\left] /5\text{ }\le \text{ } \right[3\left( 2+x \right)]/7\begin{array}{*{35}{l}} {} \\ \left( 2x\text{ }-\text{ }2 \right)/5\text{ }\le \text{ }\left( 6\text{ }+\text{ }3x...
\[\begin{array}{*{35}{l}} x/5\text{ }<\text{ }\left( 3x-2 \right)/4\text{ }-\text{ }\left( 5x-3 \right)/5 \\ x/5\text{ }<\text{ }\left[ 5\left( 3x-2 \right)\text{ }-\text{ }4\left( 5x-3...
\[\begin{array}{*{35}{l}} - \left( x\text{ }-\text{ }3 \right)\text{ }+\text{ }4\text{ }<\text{ }5\text{ }-\text{ }2x \\ -x\text{ }+\text{ }3\text{ }+\text{ }4\text{ }<\text{ }5\text{...
(3x – 2)/5 ≤ (4x – 3)/2 Multiply both the sides by 5 we get, \[\begin{array}{*{35}{l}} \left( 3x\text{ }-\text{ }2 \right)/5\text{ }\times \text{ }5\text{ }\le \text{ }\left( 4x\text{ }-\text{ }3...
\[\begin{array}{*{35}{l}} 2\text{ }\left( 3\text{ }-\text{ }x \right)\text{ }\ge \text{ }x/5\text{ }+\text{ }4 \\ 6\text{ }-\text{ }2x\text{ }\ge \text{ }x/5\text{ }+\text{ }4 \\ 6\text{ }-\text{...
\[\begin{array}{*{35}{l}} x\text{ }+\text{ }9\text{ }\ge -\text{ }x\text{ }+\text{ }19 \\ 3x\text{ }+\text{ }9\text{ }-\text{ }9\text{ }\ge \text{ }-x\text{ }+\text{ }19\text{ }-\text{ }9 \\...
\[\begin{array}{*{35}{l}} x\text{ }+\text{ }5\text{ }>\text{ }4x\text{ }-\text{ }10 \\ x\text{ }+\text{ }5\text{ }-\text{ }5\text{ }>\text{ }4x\text{ }-\text{ }10\text{ }-\text{ }5 \\...
\[\begin{array}{*{35}{l}} 3x\text{ }-\text{ }7\text{ }>\text{ }x\text{ }+\text{ }1 \\ 3x\text{ }-\text{ }7\text{ }+\text{ }7\text{ }>\text{ }x\text{ }+\text{ }1\text{ }+\text{ }7 \\ 3x\text{...
(iii) \[\begin{array}{*{35}{l}} ~x~\in ~N \\ ~2\text{ }<\text{ }5/2\text{ }<\text{ }3 \\ \end{array}\] So when, when x is a natural number, the maximum possible value of x is 2. We know that...
\[\begin{array}{*{35}{l}} 4x\text{ }-\text{ }2\text{ }<\text{ }8 \\ 4x\text{ }-\text{ }2\text{ }+\text{ }2\text{ }<\text{ }8\text{ }+\text{ }2 \\ 4x\text{ }<\text{ }10 \\ \end{array}\]...
(iii) x ∈ N As natural numbers start from 1 this implies it can never be negative, when x is a natural number, the solution of the given inequation is ∅.
-4x > 30 dividing by 4, we get \[\begin{array}{*{35}{l}} -4x/4\text{ }>\text{ }30/4 \\ -x\text{ }>\text{ }15/2 \\ x\text{ }<\text{ }\text{ }-15/2 \\ \end{array}\] (i) x ∈ R When x is...
(iii) x ∈ N When, 4 < 25/6 < 5 So when, x is a natural number, the maximum possible value of x is 4. Since,the natural numbers start from 1, the solution of the given inequation is {1, 2, 3,...
12x < 50 dividing by 12, we get \[\begin{array}{*{35}{l}} 12x/\text{ }12\text{ }<\text{ }50/12 \\ x\text{ }<\text{ }25/6 \\ \end{array}\] (i) x ∈ R When x is a real number, the solution...