Question

directions: use this information to answer parts a and b. solve the equation \\(\sqrt3{5x + 3} - 9 = -2\\). part a show each step of the solution. enter the numbers into the boxes to show the solution steps. \\(\sqrt3{5x + 3} - 9 = -2\\) \\(\sqrt3{5x + 3}\\)?=?\\(\square\\) \\(5x + 3\\)?=?\\(\square\\) \\(x\\)?=?\\(\square\\)

Explanation:

Step1: Isolate the cube root term

To isolate $\sqrt[3]{5x + 3}$, we add 9 to both sides of the equation $\sqrt[3]{5x + 3}-9=-2$.
$\sqrt[3]{5x + 3}-9 + 9=-2 + 9$
$\sqrt[3]{5x + 3}=7$

Step2: Eliminate the cube root

To eliminate the cube root, we cube both sides of the equation $\sqrt[3]{5x + 3}=7$.
$(\sqrt[3]{5x + 3})^3 = 7^3$
$5x + 3 = 343$

Step3: Solve for x

First, subtract 3 from both sides:
$5x+3 - 3=343 - 3$
$5x = 340$
Then, divide both sides by 5:
$\frac{5x}{5}=\frac{340}{5}$
$x = 68$

Answer:

For the first row (isolate cube root): $\sqrt[3]{5x + 3}\ \boldsymbol{+9=}\ 7$ (operation: add 9 to both sides, result: 7)

For the second row (eliminate cube root): $5x + 3\ \boldsymbol{=}\ 343$ (operation: cube both sides, result: 343)

For the third row (solve for x): $x\ \boldsymbol{=}\ 68$ (operation: divide by 5 after subtracting 3, result: 68)

(In boxed form for each step's result: first box 7, second box 343, third box 68)