Answer:
(a) Given, equation is \[5m=60\] Here, LHS = 5 m and RHS = 60 Now, for \[m=10,\] \[LHS=5\times 10=50\ne HS\] So, \[m=10\] does not satisfy the equation. For \[m=5,\] \[LHS=5\times 5=25\ne HS\] So, \[m=5\] does not satisfy the equation. For \[m=12\] \[LHS=5\times 12=60=RHS\] So, \[m=12\] is the solution of given equation. Form = 15, \[LHS=5\times 15=75\ne RHS\] So, \[m=15\] does not satisfy the equation. Hence, 12 is a solution of equation \[5m=60\]. (b) Given, equation is \[n+12=20\] Here, \[LHS=n+12\] and \[RHS=20\] Now, for \[n=12\] \[LHS=12+12=24\ne RHS\] So, \[n=12\] does not satisfy the equation. For \[n=8,\] \[LHS=8+12=20=RHS\] So, \[n=8\] is the solution of given equation. Now, for \[n=20,\] \[LHS=20+12=32\ne RHS\] So, \[n=20\] does not satisfy the equation. For \[n=0,\] \[LHS=0+12=12\ne RHS\] So, \[n=0\] does not satisfy the equation. Hence, \[n=8\] is a solution of equation \[n+12=20\]. (c) Given, equation is \[p-5=5\] Here, \[LHS=p-5\] and \[RHS=5\] Now, for \[p=0\], \[LHS=0-5=-5\ne RHS\] So, \[p=0\] does not satisfy the equation. For \[p=10,\] \[LHS=10-5=5=RHS\] So, \[p=10\] is the solution of given equation. Now, for \[p=5,\] \[LHS=5-5=0\ne RHS\] So, \[p=5\] does not satisfy the equation. Now, for \[p=-5,\] \[LHS=-5-5=-10,\ne RHS\] So, \[p=-5\] does not satisfy the equation. Hence, \[p=10\] is a solution of equation \[p-5=5\]. (d) Given equation is \[\frac{q}{2}=7.\] Here, \[LHS=\frac{q}{2}\] and \[RHS=7\] Now, for \[q=7,\] \[LHS=\frac{7}{2}=3\frac{1}{2}\ne RHS\] So, \[q=7\] does not satisfy the equation. Now, for \[q=2,\] \[LHS=\frac{2}{2}=1\ne RHS\] So, \[q=2\] does not satisfy the equation. Now, for\[q=10,\] \[LHS=\frac{10}{2}=5\ne RHS\] So, \[q=10\] does not satisfy the equation. For \[q=14,\] \[LHS=\frac{14}{2}=7=RHS\] So, \[q=14\]is the solution of given equation. Hence, \[q=14\] is a solution of equation \[\frac{q}{2}=7.\] (e) Given equation is \[r-4=0\] Here, \[LHS=r4\] and \[RHS=0\] Now, for \[r=-4,\] \[LHS=-4-4=-8\ne RHS\] So, \[r=-4\] is the solution of given equation. Now, for \[r=8,\] \[LHS=8-4=4\ne RHS\] So, \[r=8\] does not satisfy the equation. Now, for \[r=0,\] \[LHS=0-4=-4\ne RHS\] So, \[r=0\] does not satisfy the equation. Hence, \[r=4\] is a solution of equation \[r-4=0\]. (f) Given equation is \[x+4=2\] Here, \[LHS=x+4\] and \[RHS=2\] Now, for \[x=-2,\] \[LHS=-2+4=2=RHS\] So, \[x=-2\] is the solution of given equation. Now, for \[x=0,\] \[LHS=0+4=4\ne RHS\] So, does not satisfy the equation. Now, for \[x=2,\] \[LHS=2+4=6\ne RHS\] So, does not satisfy the equation. Now, for \[x=4,\] \[LHS=4+4=8\ne RHS\] So, \[x=4\] does not satisfy the equation. Hence, \[x=-2\]is a solution of equation \[x+4=2\].
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