Question

solve algebraically. remember to check for extraneous solutions. show your process on your own paper - you will be asked to upload your work in the next question item.
7 ( 3sqrt{x} - 8 = 7 )
8 ( sqrt{2x - 5} = 7 )
9 ( sqrt{4x + 3} + 2 = 5 )
10 ( 2sqrt{x - 7} + 4 = 18 )
11 ( sqrt{x + 2} = x - 18 )
12 ( sqrt{4x + 2} = sqrt{3x + 4} )
13 ( sqrt{x + 1} = x - 1 )
14 ( sqrt{x + 4} + 5 = 9 )
15 ( 4sqrt{x - 5} - 3 = 1 )
16 ( 0.25sqrt{2x} = 1 )

Explanation:

Let's solve problem 7: \( 3\sqrt{x} - 8 = 7 \)

Step 1: Isolate the square root term

Add 8 to both sides of the equation to isolate the square root term.
\( 3\sqrt{x} - 8 + 8 = 7 + 8 \)
\( 3\sqrt{x} = 15 \)

Step 2: Solve for \( \sqrt{x} \)

Divide both sides by 3 to solve for \( \sqrt{x} \).
\( \frac{3\sqrt{x}}{3} = \frac{15}{3} \)
\( \sqrt{x} = 5 \)

Step 3: Solve for \( x \)

Square both sides to eliminate the square root.
\( (\sqrt{x})^2 = 5^2 \)
\( x = 25 \)

Step 4: Check for extraneous solutions

Substitute \( x = 25 \) back into the original equation:
Left side: \( 3\sqrt{25} - 8 = 3(5) - 8 = 15 - 8 = 7 \)
Right side: \( 7 \)
Since both sides are equal, \( x = 25 \) is a valid solution.

Answer:

\( x = 25 \)