Q38. - Algebra 1

Question

Solve each equation. Check your solution.

$\sqrt{5-4x}-6=7$

Step-by-Step Solution

Answer

The solution of the given equation is $x=-41$.

Check:

Substitute $-41$ for x in the given equation $\sqrt{5-4x}-6=7$.

$$\begin{gathered} \sqrt{5-4x}-6=7 \\ \sqrt{5-4\left(-41\right)}-6\underset{¯}{\underset{¯}{?}}7 \\ \sqrt{5+164}-6\underset{¯}{\underset{¯}{?}}7 \\ \sqrt{169}-6\underset{¯}{\underset{¯}{?}}7 \\ 13-6\underset{¯}{\underset{¯}{?}}7 \\ 7=7 \end{gathered}$$

Therefore, $x=-41$ is the solution of the given equation $\sqrt{5-4x}-6=7$.

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} \sqrt{5-4x}-6=7 \\ \sqrt{5-4x}=7+6 \\ \sqrt{5-4x}=13 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} \sqrt{5-4x}=13 \\ {\left(\sqrt{5-4x}\right)}^2={\left(13\right)}^2\left(\text{squaring both sides}\right) \\ 5-4x=169 \\ 5-169=4x \\ -164=4x \\ \frac{-164}{4}=x \\ -41=x \end{gathered}$$

Therefore, the value of x is $-41$.

Step 3. Check the solution.

Substitute $-41$ for x in the given equation $\sqrt{5-4x}-6=7$.

$$\begin{gathered} \sqrt{5-4x}-6=7 \\ \sqrt{5-4\left(-41\right)}-6\underset{¯}{\underset{¯}{?}}7 \\ \sqrt{5+164}-6\underset{¯}{\underset{¯}{?}}7 \\ \sqrt{169}-6\underset{¯}{\underset{¯}{?}}7 \\ 13-6\underset{¯}{\underset{¯}{?}}7 \\ 7=7 \end{gathered}$$

Therefore, $x=-41$ is the solution of the given equation $\sqrt{5-4x}-6=7$.