question_answer 1)

Give the steps you will use to separate the variable and then solve the equation: (a) \[3n-2=46\]                  (b) \[5m+7=17\]                               (c) \[\frac{20p}{3}=40\]                 (d) \[\frac{3p}{10}=6\]                

Answer:

                 (a) The given equation is \[3n-2=46\] Add 2 to both sides, \[3n-2+2=46\text{ }+\text{ }2\]\[\Rightarrow \]\[3n=48\] Divide both sides by 3, \[\frac{3n}{3}=\frac{48}{3}\]\[\Rightarrow \]\[n=16\] It is the required solution. Check. Put \[n=16\] in the given equation. \[\text{L}\text{.H}\text{.S}\text{.}=3n-2=3\times 16-2\] \[=\text{48}-\text{2 }=\text{46}=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct. (b) The given equation is \[5m+7=17\] Subtract 7 from both sides, \[5m+7-7=17-7~\]\[\Rightarrow \]\[~\text{ }5m\text{ }=10\] Divide both sides by 5, \[\frac{5m}{5}=\frac{10}{5}\]      \[\Rightarrow \]\[m=2\] It is the required solution Check. Put \[m=2\] in the given equation. \[\text{L}\text{.H}\text{.S}\text{.}=5m+7=5\times 2+7\] \[=\text{1}0+\text{7}=\text{17}=\text{R}.\text{H}.\text{S}.\] as required. Hence, the solution is correct. (c) The given equation is \[\frac{20p}{3}=40\] Multiply both sides by 3, \[\frac{20p}{3}\times 3=40\times 3\] \[\Rightarrow \]\[20p=120\] Divide both sides by 20, \[\frac{20p}{20}=\frac{120}{20}\]  \[\Rightarrow \]           \[p=6\] It is the required solution. Check. Put p = 6 in the given equation. L.H.S. \[=\frac{20p}{3}=\frac{20\times 6}{3}=40=\text{R}\text{.H}\text{.S}\] as required Hence, the solution is correct. (d) The given equation is \[\frac{3p}{10}=6\] Multiply both sides by 10, \[\frac{3p}{10}\times 10=6\times 10\]  \[\Rightarrow \]\[3p=60\] Divide both side by 3, \[\frac{3p}{3}=\frac{60}{3}\]\[\Rightarrow \]\[p=20\] It is the required solution. Check. Put \[p=20\] in the given equation. \[\text{L}\text{.H}\text{.S}=\frac{3p}{10}=\frac{3\times 20}{10}=3\times 2=6=\text{R}\text{.H}\text{.S}\text{.}\] as required. Hence, the solution is correct.