question_answer 1)

Check whether the value given in the brackets is a solution to the given equation or not. (a) \[~n+5=19\left( n=1 \right)\]               (b) \[7n+5=19\text{ }\left( n=-\text{ }2 \right)\] (c) \[7n+5=19\left( n=2 \right)\]               (d) \[4p-3=13(p=1)\] (e)\[p-3=13(p=-4)\]              (f)\[~4p-3=13\,(p=0)\].                

Answer:

                (a) \[n+5=19\left( n\mathbf{ }=\mathbf{ }1 \right)\] L.H.S. \[=n+5=1+5\]             \[\left| \text{when }n\text{ }=1 \right.\]                      \[=5\] R.H.S. = 19 \[\because \]     \[\text{L}.\text{H}.\text{S}.\ne ~\text{R}.\text{H}.\text{S}.\] \[\therefore \]  \[n=1\] is not a solution to the given equation \[n+5=19\]. (b) \[7n+5=19\left( n=-2 \right)\] \[\text{L}.\text{H}.\text{S}.=\text{7n}+\text{5}=\text{7(}-\text{ 2)}+\text{5}\]  \[\left| \text{when }n=-2 \right.\]                            \[=-\text{14}+\text{5}=-\text{9}\] R.H.S. = 19 \[\because \]     \[\text{L}\text{.H}\text{.S}\text{.}\ne \text{R}\text{.H}\text{.S}\text{.}\] \[\therefore \]  \[n=-2\] is not a solution to the given equation \[7n\text{ }+\text{ }5\text{ }=\text{ }19\]. (c) \[7n+5=19(n=2)\] \[\text{L}\text{.H}\text{.S}\text{.}=7n+5=7(2)+5\]          \[\left| \text{when n = 2} \right.\]                                  \[=\text{14}+\text{5}=\text{19}=\text{R}.\text{H}.\text{S}.\] \[\therefore \]  \[\text{n}=\text{2}\]is a solution to the given equation \[7n+5=19\]. (d) \[4p-3=13(p=1)\] \[\text{L}.\text{H}.\text{S}.=\text{4p}-\text{3}=\text{4(1)}-\text{3}~\]                 \[\left| \text{when p = 1} \right.\]                                   \[=\text{4}-\text{3}=\text{1}\] \[\text{R}.\text{H}.\text{S}.=\text{13}\] \[\because \]     \[\text{L}\text{.H}\text{.S}\ne \text{R}\text{.H}\text{.S}\] \[\therefore \]  \[p=1\] is not a solution to the given equation \[4p-3=13\] (e) \[4p-3=13(p=-4)\] \[\text{L}\text{.H}\text{.S}=4p-3=4(-4)-3\]  \[\left| when\text{ }p\text{ }=-4 \right.\] \[=-16-3=-19\] \[\text{R}\text{.H}\text{.S = 13}\]                 \[\because \]     \[\text{L}\text{.H}\text{.S}\ne \text{R}\text{.H}\text{.S}\]                 \[\therefore \]  \[p=-4\] is not a solution to the given equation \[\text{4p}-\text{3}=\text{13}\]. (f) \[4p-3=13(p=0)\] L.H.S.     \[=\text{4(p)}-\text{3}=\text{4(}0\text{)}-\text{3}\]          \[\left| \text{when p = 0} \right.\]                        \[=0-\text{3}=-\text{3}\] \[\text{R}.\text{H}.\text{S}.=\text{13}\] \[\because \]     L.H.S. \[\ne \] R.H.S. \[\therefore \]  \[p=0\] is not a solution to the given equation \[\text{4p}-\text{3}=\text{13}\].