Q. 8.112 - Intermediate Algebra

Question

Solve :$\sqrt{10z+1}-2=0$

Step-by-Step Solution

Answer

The solution is,$z=\frac{3}{10}$.

Step 1 The given equation is,

$\sqrt{10z+1}-2=0$.

To isolate the radical, add $2$ on both sides.

$$\begin{gathered} \sqrt{10z+1}-2+2=0+2 \\ \sqrt{10z+1}=2 \end{gathered}$$

Now square on both sides.

$10z+1=4$

Step 2 Simplify the obtained equation.

$$\begin{gathered} 10z+1=4 \\ 10z=4-1 \\ 10z=3 \\ z=\frac{3}{10} \end{gathered}$$

Let us check the answer.

$$\begin{gathered} \sqrt{10\left(\frac{3}{10}\right)+1}-2=0 \\ \sqrt{3+1}-2=0 \\ \sqrt{4}-2=0 \\ 2-2=0 \\ 0=0 \end{gathered}$$

which is true.