Solution: Hence, \[\begin{array}{*{35}{l}} 1\text{ }\le \text{ }y\text{ }<\text{ }2 \\ \Rightarrow ~1\text{ }\le \text{ }\left| x-\text{ }\text{ }2 \right|\text{ }<\text{ }2 \\ \end{array}\]...
Solve for x, the inequalities in
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Linear Inequalities
Solve for
, where x is a positive prime number.
From the question it is given that, $2x+7\ge 5x-14$ So, by transposing we get, $5x-2x\le 14+7$ $3x\le 21$ $x\le 21/3$ $x\le 7$ As per the condition given in the question, x is a positive prime...
If ![\[p=\{x:-3<x\le 7,x\in R\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-05268769755b7bb833052e34219a78ee_l3.png "Rendered by QuickLaTeX.com")
and ![\[Q=\{x:-7\le x<3,x\in R\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7f892dba12af5188ae4f7f13aede2e54_l3.png "Rendered by QuickLaTeX.com")
represent the following solution set on the different number lines: ![\[P-Q\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e253bab8125a69c5df96614782c4817d_l3.png "Rendered by QuickLaTeX.com")
\[PQ=\left\{ -2,1,0,1,\text{ }2,3,4,5,6,7 \right\}\left\{ -7,-6,-5,-4,-3,-2,-1,0,1,2 \right\}\] \[=\left\{ 3,4,5,6,7 \right\}\]
If
and
represent the following solution set on the different number lines:(i) ![\[P\cap Q\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f2791c8e8a3d5f651198e34d473fed49_l3.png "Rendered by QuickLaTeX.com")
(ii) (ii) ![\[\mathbf{Q}\cap \mathbf{P}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2bcf017532348a436d7ff7b4353ffd0a_l3.png "Rendered by QuickLaTeX.com")
As per the condition given in the question, \[p=\{x:-3<x\le 7,x\in R\}\] So, \[P=\{-2,-1,0,1,2,3,4,5,6,7\}\] Then, \[Q=\{x:-7\le x<3,x\in R\}\] \[Q=\left\{ -7,-6,-5,-4,-3,-2,-1,0,1,2...
Solve for
, where x is a negative odd number.
From the question it is given that, $x/4+3\le x/3+4$ So, by transposing we get, $x/4-x/3\le 4-3$ $(3x-4x)/12\le 1$ $-x\le 12$ $x\ge -12$ As per the condition given in the question, x is a negative...
Solve for 
An equation between two variables that gives a straight line when plotted on a graph. From the question it is given that, $5x+3x<18-3x$ So, by transposing we get, $5x+3x<18+14$ $8x<32$...
Solve for 
From the question it is given that, $3-2x\ge x-12$ So, by transposing we get, $2x+x\le 12+3$ $3x\le 15$ $3x\le 15$ $x\le 15/3$ $x\le 5$ As per the condition given in the question, x ∈ W. Therefore,...