### Home > INT3 > Chapter 7 > Lesson 7.2.5 > Problem7-113

7-113.

Solve each of the following equations. Be sure to check your solutions.

1. $3+\frac{2x}{x+1}=5x$

To remove the denominator, multiply both sides of (or each term in) the equation by $\left(x + 1\right)$.

2. $x^{2} + 6x + 9 = 2x^{2} + 3x + 5$

$x = 4, −1$

3. $8-\sqrt{9-2x}=x+3$

Subtract $8$ from both sides and divide both sides by $−1$.

$\sqrt{9-2x}=5-x$

After setting the resulting equation equal to zero and solving the quadratic equation, $x = 4$.

Square both sides and simplify.

$\left(\sqrt{9-2x}\right)^{2}=(5-x)^2$

$9 − 2x = x^{2} − 10x + 25$