Question

42 base x +53base x = 125base x. what
is the value of x​

Answer 1

x = 7

Explanation:

The largest number is 5. Therefore x ≥ 6.

Convert numbers from x system to decimal system:

`42_x=4x+2\\\\53_x=5x+3\\\\125_x=1x^2+2x+5`

Solve the equation for x:

`42_x+53_x=125_x\Rightarrow4x+2+5x+3=x^2+2x+5\qquad\text{combine like terms}\\\\(4x+5x)+(2+3)=x^2+2x+5\\\\9x+5=x^2+2x+5\qquad\text{subtract 5 from both sides}\\\\9x=x^2+2x\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\0=x^2-7x\\\\x^2-7x=0\qquad\text{distributive}\\\\x(x-7)=0\iff x=0\ \vee\ x-7=0\\\\x=0<7\qquad\bold{it's\ not\ a\ solution}\\\\x-7=0\qquad\text{add 7 to both sides}\\\\x=7\qquad\bold{it's\ a\ solution}`