Question

What is the value of x, if twice x plus 3 cubed equals 40?

Answer 1

I will give two solutions, one where everything is cubed and one where just the 3 is cubed, because I don't know what you meant.

Just the 3 is cubed solution(Which I think is correct because it has a nicer answer):

Answer:

$13/2$

Step-by-step explanation:

We have that $2x+3^3=40$.

We can subtract $3^3=27$ from both sides of the equation to get $2x=13$.

We can then divide by $2$ to get $x=13/2$.

So, $\boxed{x=13/2}$ and we're done!

Everything is cubed solution:

Answer:

$\sqrt[3]{5}-3/2$

Step-by-step explanation:

We have that $(2x+3)^3=40$.

We can take the cube root of both sides to get $2x+3=\sqrt[3]{40}$.

Note that $40=2^3*5$, so $\sqrt[3]{40}=\sqrt[3]{2^3*5}=2\sqrt[3]{5}$.

So, we want to solve $2x+3=2\sqrt[3]{5}$.

We can subtract $3$ from both sides to get $2x=2\sqrt[3]{5}-3$.

We can then divide both sides by $2$ to get $x=\sqrt[3]{5}-3/2$.

So, $\boxed{x=\sqrt[3]{5}-3/2}$ and we're done!