Question

Solve the following equations.
(1) 17(x+4) + 8(x+6) = 11(x+5) +15(x+3)

(2) $\frac{3y}{2}$+$\frac{y+4}{4}$ = 5−$\frac{y-2}{4}$

(3) 5(1−2x) = 9(1−x)

Answer 1

(1) 17(x+4) + 8(x+6) = 11(x+5) +15(x+3)
$$\begin{gathered} \Rightarrow 17x+68+8x+48=11x+55+15x+45 \\ \Rightarrow 25x+116=26x+100 \\ \Rightarrow 26x-25x=116-100 \\ \Rightarrow x=16 \end{gathered}$$

(2) $\frac{3y}{2}$+$\frac{y+4}{4}$ = 5−$\frac{y-2}{4}$
$$\begin{gathered} 3y\times 2+y+4=20-y-2 \\ \Rightarrow 6y+y+4=18-y \\ \Rightarrow 8y=14 \\ \Rightarrow y=\frac{14}{8}=\frac{7}{4} \end{gathered}$$

(3) 5(1−2x) = 9(1−x)
$$\begin{gathered} \Rightarrow 5-10x=9-9x \\ \Rightarrow -10x+9x=9-5 \\ \Rightarrow -x=4 \\ \Rightarrow x=-4 \end{gathered}$$