Question

which value is the solution of $sqrt3{3x + 7} = 4$?

a. $-9$

b. $-1$

c. $3$

d. $19$

Explanation:

Step1: Cube both sides to eliminate the cube root

To solve the equation \(\sqrt[3]{3x + 7}=4\), we cube both sides of the equation. Cubing a cube root will cancel out the cube root operation. So, \((\sqrt[3]{3x + 7})^3 = 4^3\). This simplifies to \(3x + 7=64\) because \((\sqrt[3]{a})^3=a\) and \(4^3 = 64\).

Step2: Solve for x

Now we have the linear equation \(3x + 7 = 64\). Subtract 7 from both sides: \(3x=64 - 7\). Calculating the right side, \(64-7 = 57\), so \(3x = 57\). Then divide both sides by 3: \(x=\frac{57}{3}\). Simplifying \(\frac{57}{3}\) gives \(x = 19\).

Answer:

D. 19