Question

directions: use this information to answer parts a and b. solve the equation \\(sqrt3{x - 7} + 2 = 5\\). part a show each step of the solution. enter the numbers into the boxes to show the solution steps. show hints \\(sqrt3{x - 7} + 2 = 5\\) \\(sqrt3{x - 7}\\) ??= \\(square\\) \\(x - 7\\) ?=? \\(square\\) \\(x\\) ?=? \\(square\\)

Explanation:

Step1: Isolate the cube root term

Subtract 2 from both sides of the equation \(\sqrt[3]{x - 7}+2 = 5\) to get \(\sqrt[3]{x - 7}=5 - 2\).
\(\sqrt[3]{x - 7}=3\)

Step2: Eliminate the cube root

Cube both sides of the equation \(\sqrt[3]{x - 7}=3\) to get \(x - 7 = 3^3\).
\(x - 7 = 27\)

Step3: Solve for x

Add 7 to both sides of the equation \(x - 7 = 27\) to get \(x = 27+7\).
\(x = 34\)

Answer:

For the first box (after subtracting 2): \(3\)
For the second box (after cubing both sides): \(27\)
For the third box (after adding 7): \(34\)

The operations are: Subtract 2 (from both sides), Cube (both sides), Add 7 (to both sides) respectively.