Class VIII: Mathematics: Linear Equatation

Solve the following equations.

Q1. 20 = 6 + 2x⟹ 20 - 6 = 6 +2x-6⟹ 14 = 2x⟹ x = 14 2⟹ x = 7${\displaystyle \begin{array}{l}Q1.\\ \\ 20=6+2x\\ ⟹20-6=6+2x-6\\ ⟹14=2x\\ ⟹x=\frac{14}{2}\\ ⟹x=7\end{array}}$	Q2. 15 + x = 5x + 3 Solution: ⟹ 15 - 3 = 5x -x⟹ 12 = 4x⟹ x = 3${\displaystyle \begin{array}{l}Q2.\\ 15+x=5x+3\\ \\ Solution:\\ \\ ⟹15-3=5x-x\\ ⟹12=4x\\ ⟹x=3\end{array}}$
Q3. 3x + 2 x-6 = -7 ⟹ (3x + 2) = -7 ( x-6)⟹ 3x + 2 = -7x +42⟹ 3x + 7x = 42 -2⟹ 10x = 40⟹ x = 4${\displaystyle \begin{array}{l}Q3.\\ \\ \frac{3x+2}{x-6}=-7\\ \\ ⟹(3x{}_{}+2)=-7(x-6)\\ ⟹3x+2=-7x+42\\ ⟹3x+7x=42-2\\ ⟹10x=40\\ ⟹x=4\end{array}}$	Q4. 3a - 4 = 2(4-a)⟹3a - 4 = 8 - 2a⟹ 3a + 2a = 8 - 4⟹ 5a = 4⟹ a = 4 5${\displaystyle \begin{array}{l}Q4.\\ \\ 3a-4=2(4-a)\\ ⟹3a-4=8-2a\\ ⟹3a+2a=8-4\\ ⟹5a=4\\ ⟹a=\frac{4}{5}\end{array}}$
Q5. 3(b-4) = 2(4-b)⟹3b -12 = 8 -2b⟹ 3b + 2b = 8 + 12⟹ 5b = 20⟹ b= 4${\displaystyle \begin{array}{l}Q5.\\ \\ 3(b-4)=2(4-b)\\ ⟹3b-12=8-2b\\ ⟹3b+2b=8+12\\ ⟹5b=20\\ ⟹b=4\end{array}}$	Q6. x+2 9 = x +4 11⟹ 11 (x +2) =9 (x +4)⟹ 11x + 22 = 9x +36⟹ 11x - 9x = 36-22⟹2x = 14⟹ x =7 ${\displaystyle \begin{array}{l}Q6.\\ \\ \frac{x+2}{9}=\frac{x+4}{11}\\ ⟹11(x+2)=9(x+4)\\ ⟹11x+22=9x+36\\ ⟹11x-9x=36-22\\ ⟹2x=14\\ ⟹x=7\end{array}}$