Question

Q 7. Simplify and solve the linear equation: 0.25 (4f – 3) = 0.05 (10f – 9)

Q 9. Solve for t: $\frac{3t-2}{3}+\frac{2t+3}{2}=t+\frac{7}{6}$

Answer 1

$$\begin{gathered} \left(7\right). \\ 0.25\left(4\mathrm{f}-3\right)=0.05\left(10\mathrm{f}-9\right) \\ \Rightarrow \mathrm{f}-0.75=0.5\mathrm{f}-0.45 \\ \Rightarrow \mathrm{f}-0.5\mathrm{f}=0.75-0.45 \\ \Rightarrow 0.5\mathrm{f}=0.30 \\ \Rightarrow \mathrm{f}=\frac{0.3}{0.5}=\frac{3}{5}=0.6 \\ \left(9\right). \\ \frac{3\mathrm{t}-2}{3}+\frac{2\mathrm{t}+3}{2}=\mathrm{t}+\frac{7}{6} \\ \Rightarrow \frac{2\left(3\mathrm{t}-2\right)+3\left(2\mathrm{t}+3\right)}{6}=\frac{6\mathrm{t}+7}{6} \\ \Rightarrow 6\mathrm{t}-4+6\mathrm{t}+9=6\mathrm{t}+7 \\ \Rightarrow 12\mathrm{t}+5=6\mathrm{t}+7 \\ \Rightarrow 12\mathrm{t}-6\mathrm{t}=7-5 \\ \Rightarrow 6\mathrm{t}=2 \\ \Rightarrow \mathrm{t}=\frac{2}{6}=\frac{1}{3} \end{gathered}$$