Question

Solve each of the following equation and also check your result in each case:
(3x − 8)(3x + 2) − (4x − 11)(2x + 1) = (x − 3)(x + 7)

Answer 1

$$\begin{gathered} (3\mathrm{x}-8)(3\mathrm{x}+2)-(4\mathrm{x}-11)(2\mathrm{x}+1)=(\mathrm{x}-3)(\mathrm{x}+7) \\ \mathrm{or}9{\mathrm{x}}^2+6\mathrm{x}-24\mathrm{x}-16-8{\mathrm{x}}^2-4\mathrm{x}+22\mathrm{x}+11={\mathrm{x}}^2+7\mathrm{x}-3\mathrm{x}-21 \\ \mathrm{or}{\mathrm{x}}^2-5={\mathrm{x}}^2+4\mathrm{x}-21 \\ \mathrm{or}4\mathrm{x}=-5+21 \\ \mathrm{or}\mathrm{x}=\frac{16}{4}=4 \\ \mathrm{Thus},\mathrm{x}=4\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=4\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=(3\times 4-8)(3\times 4+2)-(4\times 4-11)(2\times 4+1)=4\times 14-5\times 9=11 \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=(4-3)(4+7)=11 \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=4. \end{gathered}$$