Answer:
[tex]x=12(\sqrt2-1)[/tex]
Step-by-step explanation:
The given equation is :
[tex]\sqrt{2} x-7+x=5[/tex]
Add 7 to both sides of the equation.
[tex]\sqrt{2} x-7+x+7=5+7\\\\\sqrt{2} x+x=12[/tex]
Taking x common from both sides of the equation.
[tex]x(\sqrt{2} +1)=12\\\\x=\dfrac{12}{\sqrt2+1}[/tex]
Multiplying both numerator and denominator by [tex]\sqrt2-1[/tex]
[tex]x=\dfrac{12}{\sqrt2+1}\times \dfrac{\sqrt2-1}{\sqrt2-1}\\\\=\dfrac{12(\sqrt2-1)}{2-1}\\\\=12(\sqrt2-1)[/tex]
Hence, the value of x is [tex]12(\sqrt2-1)[/tex].
