Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

After the first step in solving$\sqrt{2x+4}=x+5$, you would have $\underset{¯}{\text{2}x+4=x^2+10x+25}$.

Short answer

The given sentence is True.

Step-by-step solution

Step 1. Write the identity for a+b2.

The identity for${\left(a+b\right)}^2$ is:

${\left(a+b\right)}^2=a^2+2ab+b^2$

Step 2. Determine whether the given sentence is true or false.

The given equation is:

$\sqrt{2x+4}=x+5$

The given equation can be written as:

$$\begin{gathered} \sqrt{2x+4}=x+5 \\ {\left(\sqrt{2x+4}\right)}^2={\left(x+5\right)}^2\left(\text{squaringbothsides}\right) \\ 2x+4=x^2+2\left(x\right)\left(5\right)+5^2\left(\because {\left(a+b\right)}^2=a^2+2ab+b^2\right) \\ 2x+4=x^2+10x+25 \end{gathered}$$

Step 3. Conclusion

Therefore, the given sentence is true.