Question

Which equations are equivalent to ? 3^3√x+4 =12 Check all that apply.

Answer 1

Answer:

The third and the fifth equations are equivalent.

Step-by-step explanation:

First of all, you must find $x$ from $3\cdot \sqrt[3]{x+4}=12$ and check during the procedure what expressions from the options are equivalent.

The process is shown below:

1. $3\cdot \sqrt[3]{x+4}=12$
2. $\sqrt[3]{x+4}=\frac{12}{3}$
3. $\sqrt[3]{x+4}=4$
4. $(\sqrt[3]{x+4})^3=(4)^3$
5. $x+4=64$
6. $x=64-4$
7. $x=60$

From step 3, it could be said that the first, the second and the fourth options ARE NOT equivalent equations because when the left side is $\sqrt[3]{x+4}$, the right side must be $+4$, and these three options don't meet the condition.

From step 5, it could be said that the third option IS an equivalent equation because it is the same expression.

From step 7, it could be said that the fifth option IS an equivalent equation because it is the same expression.

Thus, the third and the fifth equations are equivalent.

Answer 2

Answer:

option c

x + 4 = 64

and

option e

x = 60  

Step-by-step explanation:

Given in the question an expression

3∛x+4 = 12

∛x + 4 = 12/3

∛x + 4 = 4

Take cube on both sides of the equation

∛(x + 4)³ = 4³

x + 4 = 64

x = 64 - 4

x = 60