question_answer 1)

Solve the following equations: (a) \[2(x+4)=12\]              (b) \[3(n-5)=21\]              (c) \[3(n-5)=-21\]             (d) \[-4(2+x)=8\] (e) \[4(2-x)=8\]                

Answer:

                (a) The given equation is \[2(x-4)=12\] Divide both sides by 2, \[\frac{2(x+4)}{2}=\frac{12}{2}\]\[\Rightarrow \]\[x+4=6\] Transposing 4 from L.H.S. to R.H.S., \[x=6-4\]\[\Rightarrow \]\[x=2\] It is the required solution. Check. Put \[x=2\] in the given equation. \[\text{L}.\text{H}.\text{S}.=2(x\text{ }+\text{ }4)=2(2+4)=2(6)\] \[=\text{12}=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct. (b) The given equation is \[3(n-5)=21\] Divide both sides by 3, \[\frac{3(n-5)}{3}=\frac{21}{3}\]                \[\Rightarrow \]\[n-5=7\] Transposing \[-\text{ 5}\]from L.H.S. to R.H.S., \[n=7+5\]\[\Rightarrow \]\[n=12\] It is the required solution. Check. Put \[n=12\] in the given equation. L.H.S. \[=\text{3(n }-\text{ 5)}=\text{3(12}-\text{5)}\] \[=\text{3(7)}=\text{21}\] \[=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct. (c) The given equation is \[3(n-5)=-21\] Divide both sides by 3, \[\frac{3(n-5)}{3}=-\frac{21}{3}\]              \[\Rightarrow \]\[n-5=-7\] Transposing \[-\text{ 5}\] from L.H.S. to R.H.S., \[\text{n}=-\text{7}+\text{5}\]\[\Rightarrow \] \[\text{n}=-\text{ 2}\] It is the required solution. Check. Put \[~\text{n}=-\text{ 2}\] in the given equation. \[\text{L}.\text{H}.\text{S}.=3(n-5)=3(-\text{ }2-5)=3(-\text{ }7)\] \[=-\text{ 21}=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct. (d) The given equation is \[-4(2+x)=8\] Divide both sides by\[~-\text{ 4}\], \[\frac{3(2+x)}{-4}=\frac{8}{-4}\]\[\Rightarrow \]\[2+x=-2\] Transposing 2 from L.H.S. to R.H.S., \[x=-2-2\] \[\Rightarrow \]   \[x=-4\] It is the required solution. Check. Put \[x=-\text{ }1\] in the given equation. L.H.S. \[=-\text{4(2}-\text{4)}=-\text{4(}-\text{2)}\] \[=-\text{ 8}=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct. (e) The given equation is \[4(2-x)=8\] Divide both sides by 4, \[\frac{4(2-x)}{4}=\frac{8}{4}\]\[\Rightarrow \]\[2-x=2\] Transposing 2 from L.H.S. to R.H.S., \[-x=2-2=0\]\[\Rightarrow \]\[-x=0\] Multiplying both sides by \[(-1)\] \[(-1)(-x)=(0)\times (1)=0\]         \[\Rightarrow \]\[x=0\] It is the required solution. Check. Put \[x=0\] in the given equation. L.H.S. \[=\text{4(2}-0\text{)}=\text{4(2)}\] \[=\text{8}=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct.