Chapter 2, Problem 6CR

To determine

To find: The real solutions of the equation $\sqrt{2x+3}=2$.

Answer to Problem 6CR

Solution:

$\left\{\frac{1}{2}\right\}$

Explanation of Solution

Given:

$\sqrt{2x+3}=2$

Calculation:

The given equation is $\sqrt{2x+3}=2$.

Squaring on both sides, we get

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

$2x+3=4$

Adding $-3$ on both sides of the equation, we get

$2x+3-3=4-3$

$2x=1$

$x=\frac{1}{2}$

To verify the solution:

Substituting the value of $x=\frac{1}{2}$ in the given equation, we get

$\sqrt{2x+3}=2$

$\sqrt{2\left(\frac{1}{2}\right)+3}=2$

$\sqrt{1+3}=2$

$2=2$ which is true.

$x=\frac{1}{2}$

Thus, the real solutions is $\left\{\frac{1}{2}\right\}$.