Question

Solve the equation 2x - 7 + x = 5 algebraically,and justify the solution set.

Answer 1

Consider the given equation,

$\sqrt{2x-7}+x=5$

Take the square root term on one side,

$\sqrt[]{2x-7}=5-x$

Square both sides,

$\begin{gathered} (\sqrt[]{2x-7})^2=(5-x)^2 \\ 2x-7=25+x^2-10x \end{gathered}$

Transpose and solve the like terms,

$\begin{gathered} x^2-10x-2x+25+7=0 \\ x^2-12x+32=0 \end{gathered}$

Use the method of Factorization of Middle Term,

$\begin{gathered} x^2-8x-4x+32=0 \\ x(x-8)-4(x-8)=0 \\ (x-8)(x-4)=0 \\ x-8=0\text{ }or\text{ }x-4=0 \\ x=8\text{ }or\text{ }x=4 \end{gathered}$

Thus, the solution set of the given equation is {4,8}.