Answer:
1. \[x-2=7\] We have \[x-2=7\] \[\Rightarrow \] \[x=7+2\] |Transposing ? 2 to R.H.S. \[\Rightarrow \] \[x=9\] This is the required solution. Check: L.H.S. \[=x-2=9-2\] = 7 = R.H.S. (as required) 2. \[y+3=10\] We have \[y+3=10\] \[\Rightarrow \] \[y=10-3\] | Transposing 3 to R.H.S. \[\Rightarrow \] \[y=7\] This is the required solution. Check: L.H.S. \[=y+3=7+3=10\] = R.H.S. (as required) 3. \[6=z+2\] We have \[6=z+2\] \[\Rightarrow \] \[62=z\] | Transposing 2 to L.H.S. \[\Rightarrow \] \[4=z\] \[\Rightarrow \] \[z=4\] This is the required solution. Check: R.H.S. \[=z+2=4+2=6\] = L.H.S. (as required) 4. \[\frac{3}{7}+x=\frac{17}{7}\] We have \[\frac{3}{7}+x=\frac{17}{7}\] \[\Rightarrow \] \[x=\frac{17}{7}-\frac{3}{7}\] | Transposing \[\frac{3}{7}\] to R.H.S. \[\Rightarrow \] \[x=\frac{17-3}{7}\] \[\Rightarrow \] \[x=\frac{14}{7}=2\] This is the required solution. Check: L.H.S. \[=\frac{3}{7}+x=\frac{3}{7}+2\] \[=\frac{17}{7}\,=\] R.H.S. (as required) 5. \[6x=12\] We have \[6x=12\] \[\Rightarrow \] \[x=\frac{12}{6}=2\] This is the required solution. Check: L.H.S.\[=6x=6\times 2=12\] = R.H.S. (as required) 6. \[\frac{t}{5}=10\] We have \[\frac{t}{5}=10\] \[\Rightarrow \] \[t=10\times 5=50\] | Multiplying both sides by 5 This is the required solution. Check: L.H.S. \[=\frac{t}{5}=\frac{50}{5}=10\] = R.H.S. (as required) 7. \[\frac{2x}{3}=18\] We have \[\frac{2x}{3}=18\] \[\Rightarrow \] \[2x=18\times 3\] |Multiplying both sides by 3 \[\Rightarrow \] \[2x=54\] \[\Rightarrow \] \[x=\frac{54}{2}=27\] Thus is the required solution. Check: L.H.S. \[=\frac{2x}{3}=\frac{2\times 27}{3}=18\] = R.H.S. (as required) 8. \[1.6=\frac{y}{1.5}\] We have \[1.6=\frac{y}{1.5}\] \[\Rightarrow \] \[1.6\times 1.5=y\] | Multiplying both sides by 1.5 \[\Rightarrow \] \[2.4=y\] \[\Rightarrow \] \[y=2.4\] This is the required solution. Check: RHS \[=\frac{y}{1.5}=\frac{2.4}{1.5}=1.6\] = LHS (as required) 9. \[7x-9=16\] We have \[7x-9=16\] \[\Rightarrow \] \[7x=16+9\] |Transposing ? 9 to RHS \[\Rightarrow \] \[7x=25\] \[\Rightarrow \] \[x=\frac{25}{7}\] | Dividing both sides by 7 This is the required solution. Checks: LHS \[=7x-9=7\times \frac{25}{7}-9\] \[=25-9=16=\text{RHS}\] (as required) 10. \[14y-8=13\] We have \[14y-8=13\] \[\Rightarrow \] \[14y=13+8\] | Transposing ? 8 to RHS \[\Rightarrow \] \[14y=21\] \[\Rightarrow \] \[y=\frac{21}{24}\] | Dividing both sides by 14 \[\Rightarrow \] \[y=\frac{21\div 7}{14\div 7}=\frac{3}{2}\] This is the required solution. Check: LHS \[=14y-8=14\left( \frac{3}{2} \right)-8\] \[=21-8=13\]= RHS (as required) 11. \[17+6p=9\] We have \[17+6p=9\] \[\Rightarrow \] \[6p=9-17\] | Transposing 17 to RHS \[\Rightarrow \] \[6p=-8\] \[\Rightarrow \] \[p=\frac{-8}{6}\] | Dividing both sides by 6 \[\Rightarrow \] \[p=\frac{-8\div 2}{6\div 2}\] \[\Rightarrow \] \[p=\frac{-4}{3}\] This is the required solution. Check: LHS \[=17+6p\] \[=17+6\left( \frac{-4}{3} \right)\] \[=17-8=9\] = RHS (as required) 12. \[\frac{x}{3}+1=\frac{7}{15}\] We have \[\frac{x}{3}+1=\frac{7}{15}\] \[\Rightarrow \] \[\frac{x}{3}=\frac{7}{15}-1\] |Transposing 1 to RHS \[\Rightarrow \] \[\frac{x}{3}=\frac{7-15}{15}\] \[\Rightarrow \] \[\frac{x}{3}=\frac{-8}{15}\] \[\Rightarrow \] \[x=\left( -\frac{8}{15} \right)\times 3\] | Multiplying both sides by 3 \[\Rightarrow \] \[x=\frac{-8}{5}\] This is the required solution. Check: LHS \[=\frac{x}{3}+1\] \[=\frac{1}{3}\left( \frac{-8}{5} \right)+1\] \[=\frac{-8}{15}+1\] \[=\frac{-8+15}{15}=\frac{7}{15}\] = RHS (as required)
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