Answer
$x=1$ or $x=5$
Work Step by Step
Step 1: We denote the unknown number by $x$.
Step 2: The reciprocal of x is $\frac{1}{x}$.
Step 3: 'One number plus five times its reciprocal is equal to six' means that
$x+5(\frac{1}{x})=6$
$x+(\frac{5}{x})=6$
$(x\times\frac{x}{x})+(\frac{5}{x}\times\frac{1}{1})=6$
$\frac{x^{2}}{x}+\frac{5}{x}=6$
$\frac{x^{2}+5}{x}=6$
${x^{2}+5}=6x$
$x^{2}-6x+5=0$
$x^{2}-1x-5x+5=0$
$x(x-1)-5(x-1)=0$
$(x-1)(x-5)=0$
$x=1$ or $x=5$.
