Question

Solve the following equations .

(i) $4x+\frac{1}{2}=\frac{9}{2}$ (ii) 10 = 2y + 5 (iii) 5​m $-$ 4 = 1

(iv) 6x $-$ 1 = 3x + 8 (v) 2 ( x $-$ 4) = 4x + 2 (vi) 5( x + 1 ) = 74

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)4x+\frac{1}{2}=\frac{9}{2} \\ \Rightarrow 4x=\frac{9}{2}-\frac{1}{2} \\ \Rightarrow 4x=\frac{9-1}{2} \\ \Rightarrow 4x=\frac{8}{2} \\ \Rightarrow 4x=4 \\ \Rightarrow x=\frac{4}{4} \\ \Rightarrow x=1 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{ii}\right)10=2y+5 \\ \Rightarrow 2y+5=10 \\ \Rightarrow 2y=10-5 \\ \Rightarrow 2y=5 \\ \Rightarrow y=\frac{5}{2} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)5m-4=1 \\ \Rightarrow 5m=1+4 \\ \Rightarrow 5m=5 \\ \Rightarrow m=\frac{5}{5} \\ \Rightarrow m=1 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iv}\right)6x-1=3+8 \\ \Rightarrow 6x-3x=8+1 \\ \Rightarrow 3x=9 \\ \Rightarrow x=\frac{9}{3} \\ \Rightarrow x=3 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{v}\right)2\left(x-4\right)=4x+2 \\ \Rightarrow 2\times x-2\times 4=4x+2 \\ \Rightarrow 2x-8=4x+2 \\ \Rightarrow 4x+2=2x-8 \\ \Rightarrow 4x-2x=-8-2 \\ \Rightarrow 2x=-10 \\ \Rightarrow x=-\frac{10}{2} \\ \Rightarrow x=-5 \end{gathered}$$
$$\begin{gathered} \left(\mathrm{vi}\right)5\left(x+1\right)=74 \\ \Rightarrow 5\times x+5\times 1=74 \\ \Rightarrow 5x+5=74 \\ \Rightarrow 5x=74-5 \\ \Rightarrow 5x=69 \\ \Rightarrow x=\frac{69}{5} \end{gathered}$$