Chapter 10.3, Problem 26E

To determine

To solve the equation.

Answer to Problem 26E

  $x=-1$

Explanation of Solution

Given information: $\sqrt{x+5}-\sqrt{3x+7}=0$

Formula Used: Simplify.

Calculation:

  $\sqrt{x+5}-\sqrt{3x+7}=0$

So,

  $\sqrt{x+5}=\sqrt{3x+7}$

Now, squaring both sides

  ${\left(\sqrt{x+5}\right)}^2={\left(\sqrt{3x+7}\right)}^2$

So, simplify

  $x+5=3x+7$

Now,

  $x-3x=7-5$

So, simplify

  $-2x=2$

Hence,

  $x=-1$