Question

q2) solve the equation. check your solution. $3sqrt3{4x + 9} + 6 = 381$

Explanation:

Step1: Isolate the cube root term

Subtract 6 from both sides of the equation:
$3\sqrt[3]{4x + 9} + 6 - 6 = 381 - 6$
Simplify: $3\sqrt[3]{4x + 9} = 375$

Step2: Solve for the cube root term

Divide both sides by 3:
$\frac{3\sqrt[3]{4x + 9}}{3} = \frac{375}{3}$
Simplify: $\sqrt[3]{4x + 9} = 125$

Step3: Eliminate the cube root

Cube both sides of the equation:
$(\sqrt[3]{4x + 9})^3 = 125^3$
Simplify: $4x + 9 = 1953125$

Step4: Solve for \( x \)

Subtract 9 from both sides:
$4x + 9 - 9 = 1953125 - 9$
Simplify: $4x = 1953116$

Divide both sides by 4:
$\frac{4x}{4} = \frac{1953116}{4}$
Simplify: $x = 488279$

Step5: Check the solution

Substitute \( x = 488279 \) into the original equation:
Left - hand side: $3\sqrt[3]{4(488279)+9}+6$
First, calculate inside the cube root: $4(488279)+9 = 1953116 + 9 = 1953125$
Then, $\sqrt[3]{1953125}=125$ (since $125^3 = 1953125$)
So, $3\times125 + 6 = 375+6 = 381$, which matches the right - hand side.

Answer:

\( x = 488279 \)